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

$\frac{x^2}{36} +\frac{y^2}{100} =1$

General equation is

$\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1$

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

$c=\sqrt{a^2 -b^2}$

$c=\sqrt{100 -36}= 8$

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)