Question 717120
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The foci are on the *[tex \LARGE x] axis and symmetrical to the origin, hence the center of the ellipse is at *[tex \LARGE (0,0)].


The foci of an ellipse centered at the origin with a horizontal major axis are at *[tex \LARGE (\pm{c},0)].  The *[tex \LARGE y]-intercepts of such an ellipse are at the endpoints of the minor axis, *[tex \LARGE (0,\pm{b})].  We need to find the *[tex \LARGE x]-coordinates of the endpoints of the major axis, *[tex \LARGE (\pm{a},0)].  Fortunately we know that *[tex \LARGE a], *[tex \LARGE b], and *[tex \LARGE c] are related by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ c^2\ =\ a^2\ -\ b^2]


Plugging in the values we know:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4^2\ =\ a^2\ -\ 3^2]


Solve for *[tex \LARGE a] then use the values of *[tex \LARGE a] and *[tex \LARGE b] to derive the equation of an ellipse centered at the orgin with a horizontal major axis:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^2}{a^2}\ +\ \frac{y^2}{b^2}\ =\ 1]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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