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Equations of Ellipse

Authored by Erin Inman

Mathematics

10th - 12th Grade

CCSS covered

Used 303+ times

Equations of Ellipse
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15 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

 x24+y216=1\frac{x^2}{4}+\frac{y^2}{16}=1  

 x216+y24=1\frac{x^2}{16}+\frac{y^2}{4}=1  

 x216+y264=1\frac{x^2}{16}+\frac{y^2}{64}=1  

 x264+y216=1\frac{x^2}{64}+\frac{y^2}{16}=1  

Tags

CCSS.HSG.GPE.A.1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

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

(x1)216+(y+1)236=1\frac{\left(x-1\right)^2}{16}+\frac{\left(y+1\right)^2}{36}=1

(x1)236+(y+1)216=1\frac{\left(x-1\right)^2}{36}+\frac{\left(y+1\right)^2}{16}=1

(x+1)216+(y1)236=1\frac{\left(x+1\right)^2}{16}+\frac{\left(y-1\right)^2}{36}=1

(x+1)236+(y1)216=1\frac{\left(x+1\right)^2}{36}+\frac{\left(y-1\right)^2}{16}=1

Tags

CCSS.HSG.GPE.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Media Image

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

(x+3)29+(y2)225=1\frac{\left(x+3\right)^2}{9}+\frac{\left(y-2\right)^2}{25}=1

(x3)225+(y+2)29=1\frac{\left(x-3\right)^2}{25}+\frac{\left(y+2\right)^2}{9}=1

(x3)29+(y+2)225=1\frac{\left(x-3\right)^2}{9}+\frac{\left(y+2\right)^2}{25}=1

(x+3)225+(y2)29=1\frac{\left(x+3\right)^2}{25}+\frac{\left(y-2\right)^2}{9}=1

Tags

CCSS.HSG.GPE.A.1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

 (x1)216+(y2)29=1\frac{\left(x-1\right)^2}{16}+\frac{\left(y-2\right)^2}{9}=1  

 (x+1)216+(y+2)29=1\frac{\left(x+1\right)^2}{16}+\frac{\left(y+2\right)^2}{9}=1  

 (x1)29+(y2)216=1\frac{\left(x-1\right)^2}{9}+\frac{\left(y-2\right)^2}{16}=1  

 (x+1)29+(y+2)216=1\frac{\left(x+1\right)^2}{9}+\frac{\left(y+2\right)^2}{16}=1  

Tags

CCSS.HSG.GPE.A.1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

 (x2)24+(y5)29=1\frac{\left(x-2\right)^2}{4}+\frac{\left(y-5\right)^2}{9}=1  

 (x+2)24+(y+5)29=1\frac{\left(x+2\right)^2}{4}+\frac{\left(y+5\right)^2}{9}=1  

 (x2)29+(y5)24=1\frac{\left(x-2\right)^2}{9}+\frac{\left(y-5\right)^2}{4}=1  

 (x+2)29+(y+5)24=1\frac{\left(x+2\right)^2}{9}+\frac{\left(y+5\right)^2}{4}=1  

Tags

CCSS.HSG.GPE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

 (x6)225+(y6)29=1\frac{\left(x-6\right)^2}{25}+\frac{\left(y-6\right)^2}{9}=1  

 (x+6)225+(y6)29=1\frac{\left(x+6\right)^2}{25}+\frac{\left(y-6\right)^2}{9}=1  

 (x+6)29+(y6)225=1\frac{\left(x+6\right)^2}{9}+\frac{\left(y-6\right)^2}{25}=1  

 (x6)29+(y+6)225=1\frac{\left(x-6\right)^2}{9}+\frac{\left(y+6\right)^2}{25}=1  

Tags

CCSS.HSG.GPE.A.1

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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?

 (x+3)29+(y+7)225=1\frac{\left(x+3\right)^2}{9}+\frac{\left(y+7\right)^2}{25}=1  

 (x7)29+(y3)225=1\frac{\left(x-7\right)^2}{9}+\frac{\left(y-3\right)^2}{25}=1  

 (x+7)225+(y+3)29=1\frac{\left(x+7\right)^2}{25}+\frac{\left(y+3\right)^2}{9}=1  

 (x+7)29+(y+3)225=1\frac{\left(x+7\right)^2}{9}+\frac{\left(y+3\right)^2}{25}=1  

Tags

CCSS.HSG.GPE.A.1

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