document.write( "Question 717120: Find the equation of the ellipse with the following properties.\r
\n" ); document.write( "\n" ); document.write( "The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).\r
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Algebra.Com's Answer #440105 by solver91311(24713) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "The foci are on the

axis and symmetrical to the origin, hence the center of the ellipse is at

.\r
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\n" ); document.write( "\n" ); document.write( "The foci of an ellipse centered at the origin with a horizontal major axis are at

. The

-intercepts of such an ellipse are at the endpoints of the minor axis,

. We need to find the

-coordinates of the endpoints of the major axis,

. Fortunately we know that

, and

are related by:\r
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\r
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\n" ); document.write( "\n" ); document.write( "Plugging in the values we know:\r
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\r
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\n" ); document.write( "\n" ); document.write( "Solve for

then use the values of

and

to derive the equation of an ellipse centered at the orgin with a horizontal major axis:\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "Egw to Beta kai to Sigma
\n" ); document.write( "My calculator said it, I believe it, that settles it
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$\"The$

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