## anonymous one year ago Help please? What is the equation of the ellipse with foci (2, 0), (-2, 0) and vertices (7, 0), (-7, 0)? Answer choices below.

1. anonymous

2. anonymous

@rvc @jim_thompson5910 @iambatman do you know how to do this?

3. rvc

4. Michele_Laino

we have to write an equation like this: $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ where a=7 and b is such that the subsequent condition holds: ${a^2} - {c^2} = {b^2}$ with c=2

5. Michele_Laino

so substituting c=2, and a=7 into the last equation, namely: ${a^2} - {c^2} = {b^2}$ what equation do you get?

6. rvc

@Michele_Laino thanks for helping us :)

7. anonymous

okay so $7^{2}-2^{2}=45=6.71^{2}$

8. Michele_Laino

:) @rvc

9. Michele_Laino

ok! we get: ${b^2} = 45$

10. Michele_Laino

now since a=7, then we can write: ${a^2} = 49$ am I right?

11. anonymous

yes

12. Michele_Laino

ok! next, please substitute ${a^2} = 49$ and ${b^2} = 45$ in this equation: $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ whay do you get?

13. anonymous

$\frac{ x ^{2} }{ 49}+\frac{ y ^{2} }{ 45}$

14. anonymous

=1

15. Michele_Laino

yes! that's right: $\frac{{{x^2}}}{{49}} + \frac{{{y^2}}}{{45}} = 1$

16. anonymous

thank you!