## anonymous one year ago Find the equation of an ellipse with vertices (3, 0) and (-3, 0) and foci of (2, 0) and (-2, 0). I dont know which formula to use!!! Please help me out?

1. anonymous

I know the answer to this question, its given in my textbook, but Im so confused on when to use which formula: The Major Axis Horizontal Formula? $\frac{ x ^{2} }{ a ^{2} }+\frac{ y ^{2} }{ b ^{2} }$ Or the Major Axis Vertical Formula? $\frac{ x ^{2} }{ b ^{2} }+\frac{ y ^{2} }{ a ^{2} }$

2. Jhannybean

First off, let's graph it.|dw:1439370727299:dw|

3. Jhannybean

From our formula for an ellipse, $$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}$$ we find that our center lies at $$(0,0)$$, therefore our equation turns into: $\frac{x^2}{a^2}+\frac{y^2}{b^2}$

4. anonymous

And if our center is greater than zero, we use the other formula?

5. Jhannybean

Secondly, just by graphing it, and looking at where our focus and vertices lie, we know that our ellipse is stretching horizontally, therefore $$a^2$$ corresponds with $$x$$ and $$b^2$$ corresponds with $$y$$

6. Jhannybean

We can now use the formula $$c^2=a^2+b^2$$ to find our value of b.

7. Jhannybean

We have our value of $$a$$, and that is the distance from the center to one of the vertices along the major axis. Therefore, $$a=3$$|dw:1439371651892:dw|

8. Jhannybean

$$c$$ is our distance from the center to one of the two foci. Therefore $$c=2$$|dw:1439371729613:dw|

9. Jhannybean

using the pythagorean theorem, be can find $$b$$. $c^2=a^2+b^2 \iff b^2=c^2-a^2$

10. Jhannybean

Do you see it now? With the given information, do you understand why I chose the formula I chose and how to input the information to find your equation?