Question 1

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
- x=8y2−5y+7x = 8 y ^ { 2 } - 5 y + 7x=8y2−5y+7

Accepted Answer

A)    y=5−32x−19916\mathrm { y } = \frac { 5 - \sqrt { 32 \mathrm { x } - 199 } } { 16 }y=165−32x−199c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​  and  y=5+32x−19916\mathrm { y } = \frac { 5 + \sqrt { 32 \mathrm { x } - 199 } } { 16 }y=165+32x−199c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    y=x−7−5y = \sqrt { \frac { x - 7 } { - 5 } }y=−5x−7​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z'/>​  and  y=−x−7−5y = - \sqrt { \frac { x - 7 } { - 5 } }y=−−5x−7​l0 -0c4,-6.7,10,-10,18,-10 H400000v40H1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5zM1001 80h400000v40h-400000z'/>​ 
C)    y=5−32x−1998\mathrm { y } = \frac { 5 - \sqrt { 32 \mathrm { x } - 199 } } { 8 }y=85−32x−199c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​  and  y=−5+32x−1998\mathrm { y } = - \frac { 5 + \sqrt { 32 \mathrm { x } - 199 } } { 8 }y=−85+32x−199c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
D)    y=x−7−5y = \frac { \sqrt { x - 7 } } { - 5 }y=−5x−7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​  and  y=−x−7−5y = - \frac { \sqrt { x - 7 } } { - 5 }y=−−5x−7c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​

Question 2

Graph the ellipse.
- 4(x−2) 2+9(y+1) 2=364(x-2) ^{2}+9(y+1) ^{2}=364(x−2) 2+9(y+1) 2=36

Accepted Answer

A)  
B)  
C)  
D)

Question 3

Identify the type of conic section.
-Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points  (2,0) ( 2,0 ) (2,0)   and  (−2,0) ( - 2,0 ) (−2,0)   is 21 .

Accepted Answer

A)   Ellipse
B)   Hyperbola
C)   Circle
D)   Parabola

Question 4

Graph the conic section.
-

Accepted Answer

A)  
B)  
C)  
D)

Question 5

Solve the problem.
-A projectile is thrown upward so that its distance above the ground after  ttt  seconds is  h=−14t2+560th = - 14 t ^ { 2 } + 560 \mathrm { t }h=−14t2+560t . After how many seconds does it reach its maximum height?

Accepted Answer

A)    28sec28 \mathrm { sec }28sec 
B)    40sec40 \mathrm { sec }40sec 
C)    14sec14 \mathrm { sec }14sec 
D)    20sec20 \mathrm { sec }20sec

Question 6

Write an equation for the parabola.
-vertex  (3,−7) ( 3 , - 7 ) (3,−7)  , focus  (3,−2) ( 3 , - 2 ) (3,−2)

Accepted Answer

A)    x+3=20(y+7) 2x + 3 = 20 ( y + 7 )  ^ { 2 }x+3=20(y+7) 2 
B)    20(y+7) =(x−3) 220 ( y + 7 )  = ( x - 3 )  ^ { 2 }20(y+7) =(x−3) 2 
C)    y+7=20(x+3) 2y + 7 = 20 ( x + 3 )  ^ { 2 }y+7=20(x+3) 2 
D)    20(y−7) =(x+3) 220 ( y - 7 )  = ( x + 3 )  ^ { 2 }20(y−7) =(x+3) 2

Question 7

Write an equation for the hyperbola.
-center at  (1,−8) ;( 1 , - 8 )  ;(1,−8) ;  focus at  (1−217,−8) ;( 1 - 2 \sqrt { 17 } , - 8 )  ;(1−217​,−8) ;  eccentricity  2178\frac { 2 \sqrt { 17 } } { 8 }8217​​

Accepted Answer

A)    (x−1) 24−(y+8) 264=1\frac { ( x - 1 )  ^ { 2 } } { 4 } - \frac { ( y + 8 )  ^ { 2 } } { 64 } = 14(x−1) 2​−64(y+8) 2​=1 
B)    (x+1) 264−(y−8) 24=1\frac { ( x + 1 )  ^ { 2 } } { 64 } - \frac { ( y - 8 )  ^ { 2 } } { 4 } = 164(x+1) 2​−4(y−8) 2​=1 
C)    (x−1) 264−(y+8) 24=1\frac { ( x - 1 )  ^ { 2 } } { 64 } - \frac { ( y + 8 )  ^ { 2 } } { 4 } = 164(x−1) 2​−4(y+8) 2​=1 
D)    (x+1) 24−(y−8) 264=1\frac { ( x + 1 )  ^ { 2 } } { 4 } - \frac { ( y - 8 )  ^ { 2 } } { 64 } = 14(x+1) 2​−64(y−8) 2​=1

Question 8

Solve the problem.
-The roof of a building is in the shape of the hyperbola  3y2−x2=53 \mathrm { y } ^ { 2 } - \mathrm { x } ^ { 2 } = 53y2−x2=5 , where  x\mathrm { x }x  and  y\mathrm { y }y  are in meters. Refer to the figure and determine the height,  hhh , of the outside walls.
 A=7 m\mathrm { A } = 7 \mathrm {~m}A=7 m

Accepted Answer

A)    4.2 m4.2 \mathrm {~m}4.2 m 
B)    7.3 m7.3 \mathrm {~m}7.3 m 
C)    18 m18 \mathrm {~m}18 m 
D)    54 m54 \mathrm {~m}54 m

Question 9

Write an equation for the ellipse.
-foci at  (±6,0) ;x( \pm 6,0 )  ; x(±6,0) ;x -intercepts  ±10\pm 10±10

Accepted Answer

A)    x2100+y264=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1100x2​+64y2​=1 
B)    x264+y2100=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 164x2​+100y2​=1 
C)    x28+y210=1\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 10 } = 18x2​+10y2​=1 
D)    x210+y28=1\frac { x ^ { 2 } } { 10 } + \frac { y ^ { 2 } } { 8 } = 110x2​+8y2​=1

Question 10

Write the word or phrase that best completes each statement or answers the question.
- 36y2=576−4x236 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }36y2=576−4x2

Accepted Answer

A)    xxx -intercepts  ±144\pm 144±144 ; -intercepts  ±16\pm 16±16 
B)    xxx -intercepts  ±16\pm 16±16 ;  yyy -intercepts  ±144\pm 144±144 
C)    xxx -intercepts  ±12\pm 12±12 ; -intercepts  ±4\pm 4±4 
D)    xxx -intercepts  ±4;y\pm 4 ; \mathrm { y }±4;y -intercepts  ±12\pm 12±12

Question 11

Write an equation for the parabola.
-vertex  (−6,−7) ( - 6 , - 7 ) (−6,−7)  , focus  (−6,−11) ( - 6 , - 11 ) (−6,−11)

Accepted Answer

A)    (x−6) 2=−44(y−7) ( x - 6 )  ^ { 2 } = - 44 ( y - 7 ) (x−6) 2=−44(y−7)  
B)    (x+6) 2=−16(y+7) ( x + 6 )  ^ { 2 } = - 16 ( y + 7 ) (x+6) 2=−16(y+7)  
C)    16(y−7) =(x−6) 216 ( y - 7 )  = ( x - 6 )  ^ { 2 }16(y−7) =(x−6) 2 
D)    16(y−6) =(x−7) 216 ( y - 6 )  = ( x - 7 )  ^ { 2 }16(y−6) =(x−7) 2

Question 12

Solve the problem.
-A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide,
Find the best location for the light source.

Accepted Answer

A)   1.8 m down from the top
B)   0.4 m down from the top
C)   1.2 m down from the top
D)   0.8 m down from the top

Question 13

Write an equation for the parabola with vertex at the origin.
-Through  (3,−33) ( 3 , - 3 \sqrt { 3 } ) (3,−33​)  , symmetric with respect to the  xxx -axis

Accepted Answer

A)    x2=−3yx ^ { 2 } = - \sqrt { 3 } yx2=−3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​y 
B)    y2=9xy ^ { 2 } = 9 xy2=9x 
C)    x=3y2x = \sqrt { 3 } y ^ { 2 }x=3c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​y2 
D)    x=9y2x = 9 y ^ { 2 }x=9y2

Question 14

Write an equation for the parabola with vertex at the origin.
-Focus  (0,−3) ( 0 , - 3 ) (0,−3)

Accepted Answer

A)    x2=−3yx ^ { 2 } = - 3 yx2=−3y 
B)    x2=−12yx ^ { 2 } = - 12 yx2=−12y 
C)    y2=−3xy ^ { 2 } = - 3 xy2=−3x 
D)    y2=−12xy ^ { 2 } = - 12 xy2=−12x

Question 15

Write an equation for the parabola with vertex at the origin.
-Through  (−2,2) ( - 2,2 ) (−2,2)  , opening to the left

Accepted Answer

A)    x=−2y2x = - 2 y ^ { 2 }x=−2y2 
B)    y2=−2xy ^ { 2 } = - 2 xy2=−2x 
C)    x=12y2x = \frac { 1 } { 2 } y ^ { 2 }x=21​y2 
D)    x2=2yx ^ { 2 } = 2 yx2=2y

Question 16

Write an equation for the hyperbola.
-foci at  (6−229,9) ,(6+229,9) ( 6 - 2 \sqrt { 29 } , 9 )  , ( 6 + 2 \sqrt { 29 } , 9 ) (6−229​,9) ,(6+229​,9)  ; eccentricity  22910\frac { 2 \sqrt { 29 } } { 10 }10229​​

Accepted Answer

A)    (x−6) 2100−(y−9) 216=1\frac { ( x - 6 )  ^ { 2 } } { 100 } - \frac { ( y - 9 )  ^ { 2 } } { 16 } = 1100(x−6) 2​−16(y−9) 2​=1 
B)    (y+) 2100−(x+9) 216=1\frac { ( y + )  ^ { 2 } } { 100 } - \frac { ( x + 9 )  ^ { 2 } } { 16 } = 1100(y+) 2​−16(x+9) 2​=1 
C)    (y+9) 2100−(x+6) 216=1\frac { ( y + 9 )  ^ { 2 } } { 100 } - \frac { ( x + 6 )  ^ { 2 } } { 16 } = 1100(y+9) 2​−16(x+6) 2​=1 
D)    (y−9) 2100−(x+6) 216=1\frac { ( y - 9 )  ^ { 2 } } { 100 } - \frac { ( x + 6 )  ^ { 2 } } { 16 } = 1100(y−9) 2​−16(x+6) 2​=1

Question 17

Identify the equation as a parabola, circle, ellipse, or hyperbola.
- 4x2=16−4y24 x ^ { 2 } = 16 - 4 y ^ { 2 }4x2=16−4y2

Accepted Answer

A)   Ellipse
B)   Parabola
C)   Hyperbola
D)   Circle

Question 18

Write the word or phrase that best completes each statement or answers the question.
-Explain the differences between an ellipse and a hyperbola. Both definitions emphasize
distance, but how is distance used differently in these two definitions?

Accepted Answer

Answers will vary. One possibility: An e...

Question 19

Write an equation for the ellipse.
-eccentricity  35\frac { 3 } { 5 }53​ ; vertices at  (0,−5) ,(0,5) ( 0 , - 5 )  , ( 0,5 ) (0,−5) ,(0,5)

Accepted Answer

A)    x225+y216=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 125x2​+16y2​=1 
B)    x24+y25=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 5 } = 14x2​+5y2​=1 
C)    x29+y216=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 19x2​+16y2​=1 
D)    x216+y225=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 116x2​+25y2​=1

Question 20

Find the eccentricity of the ellipse.
- x2+25y2=25x ^ { 2 } + 25 y ^ { 2 } = 25x2+25y2=25

Accepted Answer

A)    265\frac { \sqrt { 26 } } { 5 }526c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​ 
B)    26\sqrt { 26 }26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    262 \sqrt { 6 }26c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    265\frac { 2 \sqrt { 6 } } { 5 }526c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​

Exam 10: Analytic Geometry

Write an equation for the parabola with vertex at the origin. -Focus $( 0 , - 3 )$

Correct Answer
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Write an equation for the ellipse. -foci at $( \pm 6,0 ) ; x$ -intercepts $\pm 10$

Correct Answer
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Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide, Find the best location for the light source.

Correct Answer
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Write an equation for the ellipse. -eccentricity $\frac { 3 } { 5 }$ ; vertices at $( 0 , - 5 ) , ( 0,5 )$

Correct Answer
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Graph the conic section. -

Correct Answer
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Write the word or phrase that best completes each statement or answers the question. - $36 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }$

Correct Answer
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Write an equation for the hyperbola. -center at $( 1 , - 8 ) ;$ focus at $( 1 - 2 \sqrt { 17 } , - 8 ) ;$ eccentricity $\frac { 2 \sqrt { 17 } } { 8 }$

Correct Answer
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Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points $( 2,0 )$ and $( - 2,0 )$ is 21 .

Correct Answer
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Graph the ellipse. - $4(x-2) ^{2}+9(y+1) ^{2}=36$ $Graph the ellipse. - 4(x-2) ^{2}+9(y+1) ^{2}=36 A) B) C) D)$

Correct Answer
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Write an equation for the parabola. -vertex $( - 6 , - 7 )$ , focus $( - 6 , - 11 )$

Correct Answer
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Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 14 t ^ { 2 } + 560 \mathrm { t }$ . After how many seconds does it reach its maximum height?

Correct Answer
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Correct Answer
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Find the eccentricity of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Correct Answer
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Write the word or phrase that best completes each statement or answers the question. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Correct Answer
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Answers will vary. One possibility: An e...
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Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 - 4 y ^ { 2 }$

Correct Answer
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Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 8 y ^ { 2 } - 5 y + 7$

Correct Answer
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Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 3 \sqrt { 3 } )$ , symmetric with respect to the $x$ -axis

Correct Answer
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Write an equation for the parabola. -vertex $( 3 , - 7 )$ , focus $( 3 , - 2 )$

Correct Answer
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Write an equation for the parabola with vertex at the origin. -Through $( - 2,2 )$ , opening to the left

Correct Answer
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Write an equation for the hyperbola. -foci at $( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )$ ; eccentricity $\frac { 2 \sqrt { 29 } } { 10 }$

Correct Answer
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Exam 10: Analytic Geometry

Write an equation for the parabola with vertex at the origin. -Focus (0,−3) ( 0 , - 3 ) (0,−3)

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Write an equation for the ellipse. -foci at (±6,0) ;x( \pm 6,0 ) ; x(±6,0) ;x -intercepts ±10\pm 10±10

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Solve the problem. -A domed ceiling is a parabolic surface. For the best lighting on the floor, a light source is to be placed at the focus of the surface. If 9 m down from the top of the dome the ceiling is 8 m wide, Find the best location for the light source.

Correct AnswerverifiedShow Answer

Write an equation for the ellipse. -eccentricity 35\frac { 3 } { 5 }53​ ; vertices at (0,−5) ,(0,5) ( 0 , - 5 ) , ( 0,5 ) (0,−5) ,(0,5)

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Graph the conic section. -

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Write the word or phrase that best completes each statement or answers the question. - 36y2=576−4x236 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }36y2=576−4x2

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Write an equation for the hyperbola. -center at (1,−8) ;( 1 , - 8 ) ;(1,−8) ; focus at (1−217,−8) ;( 1 - 2 \sqrt { 17 } , - 8 ) ;(1−217​,−8) ; eccentricity 2178\frac { 2 \sqrt { 17 } } { 8 }8217​​

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Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points (2,0) ( 2,0 ) (2,0) and (−2,0) ( - 2,0 ) (−2,0) is 21 .

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Graph the ellipse. - 4(x−2) 2+9(y+1) 2=364(x-2) ^{2}+9(y+1) ^{2}=364(x−2) 2+9(y+1) 2=36

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Write an equation for the parabola. -vertex (−6,−7) ( - 6 , - 7 ) (−6,−7) , focus (−6,−11) ( - 6 , - 11 ) (−6,−11)

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Solve the problem. -A projectile is thrown upward so that its distance above the ground after ttt seconds is h=−14t2+560th = - 14 t ^ { 2 } + 560 \mathrm { t }h=−14t2+560t . After how many seconds does it reach its maximum height?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the eccentricity of the ellipse. - x2+25y2=25x ^ { 2 } + 25 y ^ { 2 } = 25x2+25y2=25

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Write the word or phrase that best completes each statement or answers the question. -Explain the differences between an ellipse and a hyperbola. Both definitions emphasize distance, but how is distance used differently in these two definitions?

Correct AnswerverifiedAnswers will vary. One possibility: An e...View AnswerShow Answer

Identify the equation as a parabola, circle, ellipse, or hyperbola. - 4x2=16−4y24 x ^ { 2 } = 16 - 4 y ^ { 2 }4x2=16−4y2

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Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - x=8y2−5y+7x = 8 y ^ { 2 } - 5 y + 7x=8y2−5y+7

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Write an equation for the parabola with vertex at the origin. -Through (3,−33) ( 3 , - 3 \sqrt { 3 } ) (3,−33​) , symmetric with respect to the xxx -axis

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Write an equation for the parabola. -vertex (3,−7) ( 3 , - 7 ) (3,−7) , focus (3,−2) ( 3 , - 2 ) (3,−2)

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Write an equation for the parabola with vertex at the origin. -Through (−2,2) ( - 2,2 ) (−2,2) , opening to the left

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Write an equation for the hyperbola. -foci at (6−229,9) ,(6+229,9) ( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 ) (6−229​,9) ,(6+229​,9) ; eccentricity 22910\frac { 2 \sqrt { 29 } } { 10 }10229​​

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Write an equation for the parabola with vertex at the origin. -Focus $( 0 , - 3 )$

Correct Answer
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Write an equation for the ellipse. -foci at $( \pm 6,0 ) ; x$ -intercepts $\pm 10$

Correct Answer
verified

Correct Answer
verified

Write an equation for the ellipse. -eccentricity $\frac { 3 } { 5 }$ ; vertices at $( 0 , - 5 ) , ( 0,5 )$

Correct Answer
verified

Correct Answer
verified

Write the word or phrase that best completes each statement or answers the question. - $36 \mathrm { y } ^ { 2 } = 576 - 4 \mathrm { x } ^ { 2 }$

Correct Answer
verified

Write an equation for the hyperbola. -center at $( 1 , - 8 ) ;$ focus at $( 1 - 2 \sqrt { 17 } , - 8 ) ;$ eccentricity $\frac { 2 \sqrt { 17 } } { 8 }$

Correct Answer
verified

Identify the type of conic section. -Identify the type of conic section consisting of the set of all points in the plane for which the sum of the distances from the points $( 2,0 )$ and $( - 2,0 )$ is 21 .

Correct Answer
verified

Graph the ellipse. - $4(x-2) ^{2}+9(y+1) ^{2}=36$ $Graph the ellipse. - 4(x-2) ^{2}+9(y+1) ^{2}=36 A) B) C) D)$

Correct Answer
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Write an equation for the parabola. -vertex $( - 6 , - 7 )$ , focus $( - 6 , - 11 )$

Correct Answer
verified

Solve the problem. -A projectile is thrown upward so that its distance above the ground after $t$ seconds is $h = - 14 t ^ { 2 } + 560 \mathrm { t }$ . After how many seconds does it reach its maximum height?

Correct Answer
verified

Correct Answer
verified

Find the eccentricity of the ellipse. - $x ^ { 2 } + 25 y ^ { 2 } = 25$

Correct Answer
verified

Correct Answer
verified
Answers will vary. One possibility: An e...
View Answer

Identify the equation as a parabola, circle, ellipse, or hyperbola. - $4 x ^ { 2 } = 16 - 4 y ^ { 2 }$

Correct Answer
verified

Determine the two equations necessary to graph the horizontal parabola using a graphing calculator. - $x = 8 y ^ { 2 } - 5 y + 7$

Correct Answer
verified

Write an equation for the parabola with vertex at the origin. -Through $( 3 , - 3 \sqrt { 3 } )$ , symmetric with respect to the $x$ -axis

Correct Answer
verified

Write an equation for the parabola. -vertex $( 3 , - 7 )$ , focus $( 3 , - 2 )$

Correct Answer
verified

Write an equation for the parabola with vertex at the origin. -Through $( - 2,2 )$ , opening to the left

Correct Answer
verified

Write an equation for the hyperbola. -foci at $( 6 - 2 \sqrt { 29 } , 9 ) , ( 6 + 2 \sqrt { 29 } , 9 )$ ; eccentricity $\frac { 2 \sqrt { 29 } } { 10 }$

Correct Answer
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