Question

Find the center, vertices, and foci of the ellipse with equation x squared divided by 36 plus y squared divided by 100 = 1

Answer 1

`(x^2)/(36) +(y^2)/(100) =1`

General equation is

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

Where (h,k) is the center

From the given equation h=0 and k=0

So center is (0,0)

compare the given equation with general equation

b^2 = 36 so b= 6

a^2 = 100 so a = 10

`c=√(a^2 -b^2)`

`c=√(100 -36)= 8`

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

We know h=0 , k=0 and a= 10

Vertices are (0,-10) and (0,10)

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

We know h=0 , k=0 and c=8

Foci are (0,-8) and (0,8)