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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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@rvc @jim_thompson5910 @iambatman do you know how to do this?
  • rvc
im bad at this :( @Michele_Laino could you please help here :)

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Other answers:

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
so substituting c=2, and a=7 into the last equation, namely: \[{a^2} - {c^2} = {b^2}\] what equation do you get?
  • rvc
@Michele_Laino thanks for helping us :)
okay so \[7^{2}-2^{2}=45=6.71^{2}\]
:) @rvc
ok! we get: \[{b^2} = 45\]
now since a=7, then we can write: \[{a^2} = 49\] am I right?
yes
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?
\[\frac{ x ^{2} }{ 49}+\frac{ y ^{2} }{ 45}\]
=1
yes! that's right: \[\frac{{{x^2}}}{{49}} + \frac{{{y^2}}}{{45}} = 1\]
thank you!

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