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

Answer:

Center (0,0)

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

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

Step-by-step explanation:

You are given the ellipse equation

$\dfrac{x^2}{225}+\dfrac{y^2}{625}=1$

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

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

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

$c=\sqrt{b^2-a^2}=\sqrt{625-225}=\sqrt{400}=20$

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