document.write( "Question 1088643: The center of an ellipse is on (-2, -1) and one of its vertex is on (3, -1). It the length of each latus rectum is 4, find the equation of the ellipse, its excentricity and the coordinates of its foci. \n" ); document.write( "

Algebra.Com's Answer #702956 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"$ is an ellipse with center ( $\"h\"$ , $\"k\"$ ), horizontal axis length $\"2a\"$ , and vertical axis length $\"2b\"$ ,vertices are at ( $\"h\"$ ą $\"a\"$ , $\"k\"$ ), foci is at ( $\"h\"$ ą $\"c\"$ , $\"k\"$ )\r
\n" ); document.write( "\n" ); document.write( "Note that the center is the midpoint of the segment joining the foci.\r
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\n" ); document.write( "\n" ); document.write( "if the center of an ellipse is on ( $\"-2\"$ , $\"-1\"$ ), we have $\"h=-2\"$ and $\"k=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "vertices are at ( $\"-2\"$ ą $\"a\"$ , $\"-1\"$ )=( $\"3\"$ , $\"-1\"$ )
\n" ); document.write( "=> $\"-2%2Ba=3\"$
\n" ); document.write( "=> $\"a=5+\"$ \r
\n" ); document.write( "\n" ); document.write( "foci is at ( $\"h\"$ ą $\"c\"$ , $\"k\"$ )= ( $\"-2\"$ ą $\"c\"$ , $\"-1\"$ )\r
\n" ); document.write( "\n" ); document.write( " so far, your equation is:
\n" ); document.write( " $\"%28x%2B2%29%5E2%2Fa%5E2%2B%28y%2B1%29%5E2%2Fb%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( " the length of each latus rectum is: $\"LR=4\"$
\n" ); document.write( " $\"LR=2b%5E2%2Fa\"$ => $\"4=2b%5E2%2F5\"$ => $\"20=2b%5E2\"$ => $\"b%5E2=10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c=sqrt%28a%5E2-b%5E2%29=sqrt%2825-10%29=sqrt%2815%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "foci is at:
\n" ); document.write( " ( $\"-2\"$ ą $\"sqrt%2815%29\"$ , $\"-1\"$ )=>the coordinates of its foci\r
\n" ); document.write( "\n" ); document.write( " ( $\"+1.87\"$ , $\"-1\"$ ) or ( $\"+-5.87\"$ , $\"-1\"$ )\r
\n" ); document.write( "\n" ); document.write( "your equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%5E2%2F%285%29%5E2%2B%28y%2B1%29%5E2%2F10=1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%2B2%29%5E2%2F25%2B%28y%2B1%29%5E2%2F10=1\"$ =>the equation of the ellipse\r
\n" ); document.write( "\n" ); document.write( "and, its eccentricity: $\"c%2Fa=+sqrt%2815%29%2F5\"$ ≈ $\"0.77\"$ \r
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