Find an equation of the ellipse that has center 2 3 a minor

Find an equation of the ellipse that has center (2, 3), a minor axis of length 10, and a vertex at (2. -4).

Solution

centre (2,3)

minor axis length=10

vertex =(2,-4)

The ellipse is of the form

(x-h)²/b² + (y-k)²/a²=1

b is the semi minor axis

minor axis,2b=10

therefore b=5

Vertices =(h,k+-a)

Therefore k-a=-4

k=3

Therefore 3-a=-4

a=7

Hence the required equation is

(x-2)²/25 + (y-3)²/49= 1