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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.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @rvc @jim_thompson5910 @iambatman do you know how to do this?

  3. rvc
    • one year ago
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    im bad at this :( @Michele_Laino could you please help here :)

  4. Michele_Laino
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    @Michele_Laino thanks for helping us :)

  7. anonymous
    • one year ago
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    okay so \[7^{2}-2^{2}=45=6.71^{2}\]

  8. Michele_Laino
    • one year ago
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    :) @rvc

  9. Michele_Laino
    • one year ago
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    ok! we get: \[{b^2} = 45\]

  10. Michele_Laino
    • one year ago
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    now since a=7, then we can write: \[{a^2} = 49\] am I right?

  11. anonymous
    • one year ago
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    yes

  12. Michele_Laino
    • one year ago
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    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
    • one year ago
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    \[\frac{ x ^{2} }{ 49}+\frac{ y ^{2} }{ 45}\]

  14. anonymous
    • one year ago
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    =1

  15. Michele_Laino
    • one year ago
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    yes! that's right: \[\frac{{{x^2}}}{{49}} + \frac{{{y^2}}}{{45}} = 1\]

  16. anonymous
    • one year ago
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    thank you!

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