Question

ANSWER FAST! TIMED TEST!

Find the equation of the ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)

Answer 1

`(x^2)/(144)+(y^2)/(80)=1`

Explanation:

We want to find the equation of an ellipse with foci at (8,0) and (-8,0) and a vertex at (12,0)

This is a horizontal ellipse with its center at the origin.

The equation is of the form:

`(x^2)/(a^2)+(y^2)/(b^2)=1`

Since the vertex is at (0,12)------>a=12

Since the foci is at
`(\pm8,0)`, we have c=8

Using
`a^2-b^2=c^2`

We have
`12^2-b^2=8^2`

`b^2=12^2-8^2`

`b^2=80`

Our equation now becomes:

`(x^2)/(12^2)+(y^2)/(80)=1`

Or

`(x^2)/(144)+(y^2)/(80)=1`