Question

MEDAL!
Find the center, vertices, and foci of the ellipse with equation x^2/400+y^2/625=1

Answer 1

Ok, your equation looks like this:\[\frac{ x ^{2} }{ 400 }+\frac{ y ^{2} }{ 625 }=1\]

Answer 2

yes

Answer 3

center i know is (0,0)

Answer 4

That is in the form \[\frac{ (x-h)^{2} }{ b ^{2} }+\frac{ (y-k)^{2} }{ a ^{2} }=1\]

Answer 5

You're right when you say the center is at the origin. Good. That's the first thing out of the way.

Answer 6

The second thing to remember about an ellipse is that a is ALWAYS bigger than b. So if the a (or a^2) is under the x^2, the x axis has the major vertices, and the y axis has the minor vertices.

Answer 7

Our a^2 lies under our y^2 so the y axis is the major vertex and the ellipse in general will look like this:

Answer 8

See that? If the a^2 lie under the x^2, then the x axis is the major vertex and it would look like this:

Answer 9

yes

Answer 10

(0, -25), (0, 25) would be the vertices right?

Answer 11

So you know the major vertices lie on the y axis, but where is what we need to find.

Answer 12

Wow! Yes, you'r right about the major vertices! Good job!

Answer 13

yay! thanks!

Answer 14

so do the foci land on the x axis?

Answer 15

The formula for the foci is this:\[a ^{2}-b ^{2}=c ^{2}\]And because this is a y axis ellipse, the foci lie on the y axis as well. So filling in our formula to find the foci we have this:

Answer 16

(0, -15), (0, 15) right?

Answer 17

\[625-400=c ^{2}\]

Answer 18

Yep, you're correct! Ellipses are pretty easy; they're a lot like circles. Good Job!

Answer 19

thanks!

Answer 20

The minor vertiices will lie on the x axis at (20,0) and (-20,0).

Answer 21

YW! TY for the medal!

Answer 22

just to be sure , this is it right?Center: (0, 0); Vertices: (0, -25), (0, 25); Foci: (0, -15), (0, 15)

Answer 23

just want to make sure i did not mess up the minor and major @IMStuck