document.write( "Question 951643: \"How do I write the equation for ellipse with center (3,5) , vertex (-10,5), and focus (8,5) \" \n" ); document.write( "

Algebra.Com's Answer #581200 by macston(5194) $\"\"$ $\"About$

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For an ellipse with major axis horizontal:
\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\"$
\n" ); document.write( "Where (h,k) is the center,
\n" ); document.write( "a is distance from center to vertex,
\n" ); document.write( "b is distance from center to co-vertex,
\n" ); document.write( "The co-vertex is the intersection of the ellipse and the minor axis.
\n" ); document.write( "b can also be calculated from the equation $\"b%5E2=a%5E2-c%5E2\"$ where a is distance from center to vertex, c is distance from center to focus.
\n" ); document.write( "In this case:
\n" ); document.write( "a=13 (from (3,5) to (-10, 5) the distance from 3 to -10=13
\n" ); document.write( "c=5 (from (3,5) to (8,5) the distance from 3 to 8=5
\n" ); document.write( "b=sqrt(a^2-c^2)}}}= $\"sqrt%2813%5E2-5%5E2%29=sqrt%28144%29\"$ =12
\n" ); document.write( "The equation becomes:
\n" ); document.write( " $\"%28x-3%29%5E2%2F169%2B%28y-5%29%5E2%2F144=1\"$ \n" ); document.write( "

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