Question

Can I get some help please? Thanks!

Answer 1

An ellipse (oval shape) is expressed by the following equation:

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1$ where h is the x coordinate of the center and k is the y coordinate of the center. Furthermore, a is the horizontal distance from the center, and b is the vertical distance from the center. Lastly, c is the distance from the center to one of the foci (they are spaced apart equally).

We can find the foci by using $a^2 - b^2 = c^2$

36 - 11 = $c^2$

$c = \sqrt{25} = 5$

Since the k value in this case is 0, the y value of both foci are 0. Also, since h and k are both 0, we know the center of the ellipse is at the origin.

So the foci are (-5, 0) and (5, 0)

Hope this helps :)