Equations of Ellipse

An ellipse centered at the origin has a vertical major axis length of 8 units and an horizontal minor axis length of 4. What is the equation of the ellipse?

•  $\frac{x^2}{4}+\frac{y^2}{16}=1$  

•  $\frac{x^2}{16}+\frac{y^2}{4}=1$  

•  $\frac{x^2}{16}+\frac{y^2}{64}=1$  

•  $\frac{x^2}{64}+\frac{y^2}{16}=1$  

Tags

CCSS.HSG.GPE.A.3

The graph of an ellipse is shown. Which equation represents this ellipse?

• $\frac{\left(x-1\right)^2}{16}+\frac{\left(y+1\right)^2}{36}=1$

• $\frac{\left(x-1\right)^2}{36}+\frac{\left(y+1\right)^2}{16}=1$

• $\frac{\left(x+1\right)^2}{16}+\frac{\left(y-1\right)^2}{36}=1$

• $\frac{\left(x+1\right)^2}{36}+\frac{\left(y-1\right)^2}{16}=1$

Tags

CCSS.HSG.GPE.A.3

The graph of an ellipse is shown. Which equation represents this ellipse?

• $\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1$

• $\frac{\left(x-3\right)^2}{25}+\frac{\left(y+2\right)^2}{9}=1$

• $\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{25}=1$

• $\frac{\left(x+3\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1$

Tags

CCSS.HSG.GPE.A.3

An ellipse has vertices at (-3, 2) and (5, 2) and co-vertices at (1, -1) and (1, 5). What is the equation of the ellipse?

•  $\frac{\left(x-1\right)^2}{16}+\frac{\left(y-2\right)^2}{9}=1$  

•  $\frac{\left(x+1\right)^2}{16}+\frac{\left(y+2\right)^2}{9}=1$  

•  $\frac{\left(x-1\right)^2}{9}+\frac{\left(y-2\right)^2}{16}=1$  

•  $\frac{\left(x+1\right)^2}{9}+\frac{\left(y+2\right)^2}{16}=1$  

Tags

CCSS.HSG.GPE.A.3

An ellipse has vertices at (2, 2) and (2, 8) and co-vertices at (0, 5) and (4, 5). What is the equation of the ellipse?

•  $\frac{\left(x-2\right)^2}{4}+\frac{\left(y-5\right)^2}{9}=1$  

•  $\frac{\left(x+2\right)^2}{4}+\frac{\left(y+5\right)^2}{9}=1$  

•  $\frac{\left(x-2\right)^2}{9}+\frac{\left(y-5\right)^2}{4}=1$  

•  $\frac{\left(x+2\right)^2}{9}+\frac{\left(y+5\right)^2}{4}=1$  

Tags

CCSS.HSG.GPE.A.3

An ellipse has vertices at (-1, 6) and (-11, 6) and foci at (-2, 6) and (-10, 6). What is the equation of the ellipse?

•  $\frac{\left(x-6\right)^2}{25}+\frac{\left(y-6\right)^2}{9}=1$  

•  $\frac{\left(x+6\right)^2}{25}+\frac{\left(y-6\right)^2}{9}=1$  

•  $\frac{\left(x+6\right)^2}{9}+\frac{\left(y-6\right)^2}{25}=1$  

•  $\frac{\left(x-6\right)^2}{9}+\frac{\left(y+6\right)^2}{25}=1$  

Tags

CCSS.HSG.GPE.A.3

An ellipse has co-vertices at (-4, -3) and (-10, -3) and foci at (-7,  1) and (-7, -7). What is the equation of the ellipse?

•  $\frac{\left(x+3\right)^2}{9}+\frac{\left(y+7\right)^2}{25}=1$  

•  $\frac{\left(x-7\right)^2}{9}+\frac{\left(y-3\right)^2}{25}=1$  

•  $\frac{\left(x+7\right)^2}{25}+\frac{\left(y+3\right)^2}{9}=1$  

•  $\frac{\left(x+7\right)^2}{9}+\frac{\left(y+3\right)^2}{25}=1$  

Tags

CCSS.HSG.GPE.A.3

An ellipse has the following set of characteristics:

Vertices ( 4, 3), (4, - 9)

Length of minor axis is 8

What is the center of this ellipse?

• (4, 6)

• ( - 4, 3)

• (6, 4)

• (4, -3)

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( -7, -3), (13, - 3)
foci ( - 5, -3 ) , (11 , -3)
what is the a and b value of the ellipse?

• a = 10 , b = 6
• a = 6 , b = 10
• a = 36 , b = 100
• a = 100 , b = 36

Tags

CCSS.HSG.GPE.A.3

What are the foci of the shifted ellipse?

• (-5,1) and (-1,1)

• (±√3,0)

• (0,1) and (-6,1)

• $\left(-3\pm\sqrt{3},\ 1\right)$

Tags

CCSS.HSG.GPE.A.3