Question

18. Find the center, vertices, and foci of the ellipse with equation x squared divided by 225 plus y squared divided by 625 = 1. (5 points)

Answer 1

Center (0,0)

Vertices (-15,0), (15,0), (0,-25), (0,25)

Foce (0,-20), (0,20)

Explanation:

You are given the ellipse equation

`(x^2)/(225)+(y^2)/(625)=1`

The canonical equation of ellipse with center at (0,0) is

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

So,

`a^2=225\Rightarrow a=15\\ \\b^2=625\Rightarrow b=25`

Hence, the center of your ellipse is at (0,0) and the vertices are at points (-15,0), (15,0), (0,-25) and (0,25)

This ellipse is strengthen in y-axis, so

`c=√(b^2-a^2)=√(625-225)=√(400)=20`

and the foci are at points (0,-20) and (0,20).