Question

What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)?

Answer 1

Given ellipse foci (0,4),(0,-4)

given ellipse is vertical ellipse.

(x-h)^2/a^2+(y-k)^2/b^2 = 1

Center (h,k)

Vertices are (h,k+a) , (h,k-a)

Focal distance c = sqrt(a^2-b^2)

Foci (h,k+c),(h,k-c)

Center = (h,k) = (0,0)

Foci (0,4),(0,-4)

Vertices are (0,8),(0-8)

We can able to write a = 8

c = 4

c = sqrt(a^2-b^2)

c^2 = a^2-b^2

16 = 64-b^2

64-16 = b^2

48 = b^2

Equation of ellipse is x^2/48+y^2/64 = 1