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

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

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