ExplainItLikeImFive
  • ExplainItLikeImFive
Find the standard form of the equation of the ellipse satisfying the given conditions. Foci: (0, -2), (0, 2); y-intercepts: -5 and 5
Precalculus
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katieb
  • katieb
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ExplainItLikeImFive
  • ExplainItLikeImFive
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anonymous
  • anonymous
Using your standard equation of an ellipse for b>a: \[\large \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\] Where: "a" is the minor axis "b" is the major axis In your question, you're given the coordinates of the foci, S, and y-intercepts i.e the value of "b". \[\large S(0, \pm be)\] where: "e" is the eccentricity \[\large y=\pm 5\] By connecting the-coordinates of the foci and the y-intercepts, you can find the value of "e". Let's take the positive case for both the foci and y-intercepts. Therefore: \[be=2\] \[b=5\] \[5e=2\] \[e=\frac{2}{5}\]
anonymous
  • anonymous
By connecting the y-coordinates*

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anonymous
  • anonymous
By using this equation: \[a^2=b^2(1-e^2) You can find the value of "a" and thus form your standard equation of the ellipse.
anonymous
  • anonymous
\[a^2=b^2(1-e^2)\]
ExplainItLikeImFive
  • ExplainItLikeImFive
Thanks

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