Question

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

Answer 1

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

Answer 2

im bad at this :(
@Michele_Laino could you please help here :)

Answer 3

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

Answer 4

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

Answer 5

@Michele_Laino thanks for helping us :)

Answer 6

okay so \[7^{2}-2^{2}=45=6.71^{2}\]

Answer 7

:) @rvc

Answer 8

ok! we get:
\[{b^2} = 45\]

Answer 9

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

Answer 10

yes

Answer 11

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?

Answer 12

\[\frac{ x ^{2} }{ 49}+\frac{ y ^{2} }{ 45}\]

Answer 13

=1

Answer 14

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

Answer 15

thank you!