Question

What is the equation of the ellipse with foci (7, 0), (-7, 0) and co-vertices (0, 3), (0, -3)?

	A.
	B.
	C.
	D.

 

Answer 1

The foci of ellipse = (7, 0) and (-7, 0)

The y coordinate of foci is same.

co - vertices are (0, 3) and (0, -3)

The x coordinate of co - vertices are same.

So the ellipse is horizontal.

Standard form of ellipse

 where

co - vertices are (h, k + b) , (h , k - b ) = (0, 3), (0 , -3)

Therefore, x  coordinate of vertex = 0

h  = 0

k + b  = 3 ---> (1)

k - b  = -3 ---> (2)

Add the equations (1) & (2).

2k = 0

k  = 0

Substitute k = 0 in equation (1).

b  = 3

(h, k) = (0, 0)

Foci  (h + c, k ) , (h - c, k ) = (7, 0) , (-7, 0)

Therfore c = 7

Substitute the above values in standard form.

Option B is correct choice.