Question 1

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure).   Using the coordinate system shown,find an equation for the ellipse. ​

Accepted Answer

A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 6 } = 1$ 
A)  $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 4 } = 1$ 
B)  $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$ 
C)  $$\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 9 } = 1$$ 
D)  $\frac { x ^ { 2 } } { 9 } - \frac { y ^ { 2 } } { 4 } = 1$ 
E)  $\frac { x ^ { 2 } } { 4 } - \frac { y ^ { 2 } } { 6 } = 1$

Question 2

Find the center and vertices of the ellipse.​ $x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0$ ​

Accepted Answer

A) center: $( - 1 , - 8 )$ vertices: $( - 4 , - 8 ) , ( 9 , - 8 )$ 
B) center: $( 8,1 )$ vertices: $( 7,1 ) , ( 9,1 )$ 
C) center: $( - 8 , - 1 )$ vertices: $( - 9 , - 1 ) , ( - 7 , - 1 )$ 
D) center: $( - 8 , - 1 )$ vertices: $( - 11 , - 1 ) , ( - 5 , - 1 )$ 
E) center: $( 8,1 )$ vertices: $( 5,1 ) , ( - 11,1 )$ 
A) center: $( - 1 , - 8 )$ vertices: $( - 4 , - 8 ) , ( 9 , - 8 )$ 
B) center: $( 8,1 )$ vertices: $( 7,1 ) , ( 9,1 )$ 
C) center: $( - 8 , - 1 )$ vertices: $( - 9 , - 1 ) , ( - 7 , - 1 )$ 
D) center: $( - 8 , - 1 )$ vertices: $( - 11 , - 1 ) , ( - 5 , - 1 )$ 
E) center: $( 8,1 )$ vertices: $( 5,1 ) , ( - 11,1 )$

Question 3

Sketch the graph of the ellipse,using the latera recta.​ $$\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 4

Find the standard form of the equation of the ellipse with the given characteristics. ​
Center: $( 15,5 )$ ;a = 3b;Foci: $( 5,5 ) , ( 25,5 )$ ,where a - thr semimajor axis,b - semiminor axis.
​

Accepted Answer

A)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y - 5 ) ^ { 2 } } { 200 } = 1$ 
B)  $\frac { x ^ { 2 } } { 225 } - \frac { ( y - 5 ) ^ { 2 } } { 200 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 200 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 200 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 200 } = 1$ 
A)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y - 5 ) ^ { 2 } } { 200 } = 1$ 
B)  $\frac { x ^ { 2 } } { 225 } - \frac { ( y - 5 ) ^ { 2 } } { 200 } = 1$ 
C)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { y ^ { 2 } } { 200 } = 1$ 
D)  $\frac { ( x - 5 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 200 } = 1$ 
E)  $\frac { ( x + 5 ) ^ { 2 } } { 225 } + \frac { ( y + 5 ) ^ { 2 } } { 200 } = 1$

Question 5

Find the center and vertices of the ellipse.​ $$\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } = 1$$ ​

Accepted Answer

A) center: (9,6)vertices: (-9,-6), (9,6) 
B) center: (0,0)vertices: (0,-9), (0,9) 
C) center: (9,0)vertices: (0,-6), (0,6) 
D) center: (0,0)vertices: (-6,0), (6,0) 
E) center: (0,0)vertices: (-9,0), (9,0) 
A) center: (9,6)vertices: (-9,-6), (9,6) 
B) center: (0,0)vertices: (0,-9), (0,9) 
C) center: (9,0)vertices: (0,-6), (0,6) 
D) center: (0,0)vertices: (-6,0), (6,0) 
E) center: (0,0)vertices: (-9,0), (9,0)

Question 6

Identify the conic as a circle or an ellipse.​ $$x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0$$ ​

Accepted Answer

A) Circle 
B) Ellipse 
A) Circle 
B) Ellipse

Question 7

Sketch the graph of the ellipse,using the latera recta.​ $$9 x ^ { 2 } + 4 y ^ { 2 } = 36$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 8

Match the equation with its graph. $$x ^ { 2 } + 9 y ^ { 2 } = 9$$

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Exam 61: Ellipses

An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown,find an equation for the ellipse. ​

Find the center and vertices of the ellipse.​ x2+9y2+16x+18y+64=0x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0x2+9y2+16x+18y+64=0 ​

Sketch the graph of the ellipse,using the latera recta.​ x24+y216=1\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 14x2​+16y2​=1 ​

Find the standard form of the equation of the ellipse with the given characteristics. ​ Center: (15,5)( 15,5 )(15,5) ;a = 3b;Foci: (5,5),(25,5)( 5,5 ) , ( 25,5 )(5,5),(25,5) ,where a - thr semimajor axis,b - semiminor axis. ​

Find the center and vertices of the ellipse.​ x281+y236=1\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } = 181x2​+36y2​=1 ​

Identify the conic as a circle or an ellipse.​ x2+y2−3x+4y−2=0x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0x2+y2−3x+4y−2=0 ​

Sketch the graph of the ellipse,using the latera recta.​ 9x2+4y2=369 x ^ { 2 } + 4 y ^ { 2 } = 369x2+4y2=36 ​

Match the equation with its graph. x2+9y2=9x ^ { 2 } + 9 y ^ { 2 } = 9x2+9y2=9

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An elliptical stained-glass insert is to be fitted in a 4ft by 6ft rectangular opening (see figure). Using the coordinate system shown,find an equation for the ellipse.

Find the center and vertices of the ellipse. $x ^ { 2 } + 9 y ^ { 2 } + 16 x + 18 y + 64 = 0$

Sketch the graph of the ellipse,using the latera recta. $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Find the standard form of the equation of the ellipse with the given characteristics. Center: $( 15,5 )$ ;a = 3b;Foci: $( 5,5 ) , ( 25,5 )$ ,where a - thr semimajor axis,b - semiminor axis.

Find the center and vertices of the ellipse. $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 36 } = 1$

Identify the conic as a circle or an ellipse. $x ^ { 2 } + y ^ { 2 } - 3 x + 4 y - 2 = 0$

Sketch the graph of the ellipse,using the latera recta. $9 x ^ { 2 } + 4 y ^ { 2 } = 36$

Match the equation with its graph. $x ^ { 2 } + 9 y ^ { 2 } = 9$