35.2k views
4 votes
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)

1 Answer

5 votes

Answer:

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).

User Reii Nakano
by
8.4k points

Related questions

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories