document.write( "Question 1170502: Find an equation for the ellipse that satisfies the given conditions.
\n" ); document.write( "Endpoints of major axis:
\n" ); document.write( "(±9, 0), distance between foci: 8 \n" ); document.write( "

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\n" ); document.write( "The endpoints of the major axis are (-9,0) and (9,0), so the center of the ellipse is (0,0) and the semi-major axis is 9. The equation is then of the form

\n" ); document.write( " $\"x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1\"$

\n" ); document.write( "a is the semi-major axis and b is the semi-minor axis; a and b are related by

\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( "Since the distance between the two foci is 8, the distance from the center to each focus is 4.

\n" ); document.write( "So $\"c%5E2+=+a%5E2-b%5E2\"$ , with a=9 and c=4. a^2=81; use that to determine b^2. Then plug the a^2 and b^2 numbers into the equation.

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