Question

Which of the following equations is of an ellipse with x-intercepts of (3, 0) and (-3, 0) and y-intercepts at (0, 1) and (0, -1)?
https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p12a.gif

https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p12b.gif

https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p12c.gif

Answer 1

Do you know the general formula for an ellipse?

Answer 2

no

Answer 3

Ok, it looks like this: and I will try and explain to you what it means as best as I can:

Answer 4

ok

Answer 5

\[\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }=1\]

Answer 6

This is for an ellipse that is centered at the origin, which yours is, so let's not get into moving the center.

Answer 7

One thing to remember about a and b is that a is ALWAYS greater than b, AND that a will always be under the major vertex. The major vertex is the one that is larger. Your graph looks something like this, using the points you provided:

Answer 8

As you can see, the x axis is the major vertex. Therefore, the a term goes under the x^2 and the b term goes under the y^2 term.

Answer 9

If a = 3, then a^2 = 9; likewise, if b = 1, then b^2 = 1. So our equation for this ellipse would be\[\frac{ x ^{2} }{ 9 }+\frac{ y ^{2} }{ 1 }=1\]

Answer 10

Thank you

Answer 11

can you help me with another equation?

Answer 12

Yes I can. Sorry I was gone for so long. tutor.com called me to help another student! I'm here now! WHatcha got?

Answer 13

TY for the medal!

Answer 14

It's ok. You welcome. A hyperbola with center at (0, 0), with x-intercepts at (4, 0) and (-4, 0), with b = 1, and opening horizontally has the equation
https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p15a.gif
https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p15b.gif
https://media.glynlyon.com/g_alg02_ccss_2013/8/m11u7q2p15c.gif

Answer 15

@IMStuck

Answer 16

I'm looking at your answer choices now to see which matches up and then I will work on explaining to you. Ok?

Answer 17

ok

Answer 18

Alright, the thing with hyperbolas is that the x^2 and the y^2 terms move and the a and the b remain in their places. Unlike in an ellipse, where the a and the b move under whichever vertex is the major (that would be a) and whichever vertex is the minor (that would be b). Here, the x^2 and y^2 terms move. The way the hyperbola is opening tells you which comes first, either the x^2 or the y^2. Here in this one your vertices are on the x axis, so the hyperbola is an x^2 hyperbola.

Answer 19

That means that the x^2 term comes first and the y^2 term comes second. There is ALWAYS a subtraction sign in a hyperbola, just like in an ellipse, there is ALWAYS a plus sign. So with that being said, and the fact that your hyperbola has a center of (0,0), we have this so far:

Answer 20

\[\frac{ x ^{2} }{ a ^{2} }-\frac{ y ^{2} }{ b ^{2} }=1\]

Answer 21

If this an x^2 hyperbola it will look something like this (bear with my art work, here, please!):

Answer 22

those are your vertices for the hyperbola and it fits in like this: