document.write( "Question 1169055: Find the equation of the ellipse if the vertex is at (5,1) and foci at (-2,1) and (4,1). express your answer in general form \n" ); document.write( "

Algebra.Com's Answer #794160 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The foci are at (-2,1) and (4,1), so the center is at (1,1), and the major axis is horizontal. The general equation is

\n" ); document.write( " $\"%28x-1%29%5E2%2Fa%5E2%2B%28y-1%29%5E2%2Fb%5E2=1\"$

\n" ); document.write( "a is the semi-major axis (distance between center and each vertex); b is the semi-minor axis. a and b are related by the equation

\n" ); document.write( " $\"c%5E2=a%5E2-b%5E2\"$

\n" ); document.write( "where c is the distance from the center to each focus.

\n" ); document.write( "With the given information, we know a=4 and c=3, so a^2=16 and c^2=9, giving us b^2=16-9=7.

\n" ); document.write( "The equation is

\n" ); document.write( " $\"%28x-1%29%5E2%2F16%2B%28y-1%29%5E2%2F7=1\"$
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