Question 1

Find the eccentricity of the ellipse.
-$$4 x ^ { 2 } + y ^ { 2 } = 36$$

Accepted Answer

A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $\sqrt { 5 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\sqrt { 3 }$ 
A)  $\frac { \sqrt { 5 } } { 2 }$ 
B)  $\sqrt { 5 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\sqrt { 3 }$

Question 2

Find the center, foci, and asymptotes of the hyperbola.
-$$x ^ { 2 } - y ^ { 2 } = 162$$

Accepted Answer

A)  C: (0,0); F: (18, 0), $( - 18,0 )$; A: $y = 2 x , y = - 2 x$ 
B)  C: $( 0,0 )$; F: $( 9,0 ) , ( - 9,0 )$; A: $y = x , y = - x$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( 18,0 ) , ( - 18,0 ) ; \mathrm { A } : \mathrm { y } = \mathrm { x } , \mathrm { y } = - \mathrm { x }$ 
D)  C: $( 2,2 ) ; F : ( 18,0 ) , ( - 18,0 ) ; A : y = 2 x , y = - 2 x$ 
A)  C: (0,0); F: (18, 0), $( - 18,0 )$; A: $y = 2 x , y = - 2 x$ 
B)  C: $( 0,0 )$; F: $( 9,0 ) , ( - 9,0 )$; A: $y = x , y = - x$ 
C)  C: $( 0,0 ) ; \mathrm { F } : ( 18,0 ) , ( - 18,0 ) ; \mathrm { A } : \mathrm { y } = \mathrm { x } , \mathrm { y } = - \mathrm { x }$ 
D)  C: $( 2,2 ) ; F : ( 18,0 ) , ( - 18,0 ) ; A : y = 2 x , y = - 2 x$

Question 3

Choose the equation that matches the graph.
-

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 9 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 49 } = 1$ 
B)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 49 } = 1$ 
C)  $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$ 
D)  $\frac { x ^ { 2 } } { 49 } - \frac { y ^ { 2 } } { 9 } = 1$

Question 4

Write an equation for the hyperbola.
-vertices at $( - 5,3 ) , ( - 5 , - 19 ) ;$ asymptotes $y = \pm \frac { 11 } { 4 } ( x + 5 ) - 8$

Accepted Answer

A)  $\frac { ( y - 8 ) ^ { 2 } } { 121 } - \frac { ( x - 5 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 121 } - \frac { ( y - 8 ) ^ { 2 } } { 121 } = 1$ 
C)  $\frac { ( y + 8 ) ^ { 2 } } { 121 } - \frac { ( x + 5 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y + 8 ) ^ { 2 } } { 121 } = 1$ 
A)  $\frac { ( y - 8 ) ^ { 2 } } { 121 } - \frac { ( x - 5 ) ^ { 2 } } { 16 } = 1$ 
B)  $\frac { ( x - 5 ) ^ { 2 } } { 121 } - \frac { ( y - 8 ) ^ { 2 } } { 121 } = 1$ 
C)  $\frac { ( y + 8 ) ^ { 2 } } { 121 } - \frac { ( x + 5 ) ^ { 2 } } { 16 } = 1$ 
D)  $\frac { ( x + 5 ) ^ { 2 } } { 121 } - \frac { ( y + 8 ) ^ { 2 } } { 121 } = 1$

Question 5

Find the eccentricity of the hyperbola.
-$$8 x ^ { 2 } - 9 y ^ { 2 } = 72$$

Accepted Answer

A)  $\frac { \sqrt { 13 } } { 3 }$ 
B)  $\frac { \sqrt { 17 } } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 3 } { 2 }$ 
A)  $\frac { \sqrt { 13 } } { 3 }$ 
B)  $\frac { \sqrt { 17 } } { 3 }$ 
C)  $\frac { 1 } { 2 }$ 
D)  $\frac { 3 } { 2 }$

Question 6

Solve the problem.
-A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 430 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the
Moon varies from 892 km to 979 km.

Accepted Answer

A)  $\frac { x ^ { 2 } } { 1322 ^ { 2 } } + \frac { y ^ { 2 } } { 1409 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 892 } + \frac { y ^ { 2 } } { 979 } = 1$ 
C)  $\frac { x ^ { 2 } } { 14092 } + \frac { y ^ { 2 } } { 1322 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 979 } + \frac { y ^ { 2 } } { 892 } = 1$ 
A)  $\frac { x ^ { 2 } } { 1322 ^ { 2 } } + \frac { y ^ { 2 } } { 1409 ^ { 2 } } = 1$ 
B)  $\frac { x ^ { 2 } } { 892 } + \frac { y ^ { 2 } } { 979 } = 1$ 
C)  $\frac { x ^ { 2 } } { 14092 } + \frac { y ^ { 2 } } { 1322 ^ { 2 } } = 1$ 
D)  $\frac { x ^ { 2 } } { 979 } + \frac { y ^ { 2 } } { 892 } = 1$

Find the eccentricity of the ellipse. - $4 x ^ { 2 } + y ^ { 2 } = 36$

Find the center, foci, and asymptotes of the hyperbola. - $x ^ { 2 } - y ^ { 2 } = 162$

Choose the equation that matches the graph. -

Write an equation for the hyperbola. -vertices at $( - 5,3 ) , ( - 5 , - 19 ) ;$ asymptotes $y = \pm \frac { 11 } { 4 } ( x + 5 ) - 8$

Find the eccentricity of the hyperbola. - $8 x ^ { 2 } - 9 y ^ { 2 } = 72$

Solve the problem. -A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius of 430 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the Moon varies from 892 km to 979 km.

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Exam 10: Analytic Geometry

Find the eccentricity of the ellipse. - 4x2+y2=364 x ^ { 2 } + y ^ { 2 } = 364x2+y2=36

Find the center, foci, and asymptotes of the hyperbola. - x2−y2=162x ^ { 2 } - y ^ { 2 } = 162x2−y2=162