document.write( "Question 280514: write an equation for the ellipse with end points of the major axis at (7,1) and (-7,1) and end points of the minor axis at (0,5) and (0,-3). plz explain step by step...thnx \n" ); document.write( "

Algebra.Com's Answer #204001 by jsmallt9(3758) $\"\"$ $\"About$

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The general form of the equation for an ellipse is:
\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1\"$ for horizontally oriented ellipses
\n" ); document.write( "or
\n" ); document.write( " $\"%28x-h%29%5E2%2Fb%5E2+%2B+%28y-k%29%5E2%2Fa%5E2+=+1\"$ for vertically oriented ellipses
\n" ); document.write( "where
\n" ); document.write( "(h, k) is the center of the ellipse
\n" ); document.write( "a = the distance from the center to a vertex on the major axis
\n" ); document.write( "b = the distance from the center to a vertex on the minor axis

\n" ); document.write( "Since the vertices on the major axis, (7,1) and (-7,1), are on the same horizontal line, this is a horizontally oriented ellipse. So we will use the first general form.

\n" ); document.write( "The center of an ellipse is the midpoint between the vertices on either the major or minor axis. The midpoint between (7,1) and (-7,1) (or between (0, 5) and (0, -3)) is (0, 1). So the center is (0, 1) and h = 0 and k = 1.

\n" ); document.write( "From the center, (0, 1), to either vertex on the major axis ((7, 1) or (-7, 0)) is 7. So a = 7.

\n" ); document.write( "From the center, (0, 1), to either vertex on the minor axis ((0, 5) or (0, -3)) is 4. So b = 4.

\n" ); document.write( "Now that we know h, k, a and b we can write the equation:
\n" ); document.write( " $\"%28x-%280%29%29%5E2%2F%287%29%5E2+%2B+%28y-%281%29%29%5E2%2F%284%29%5E2+=+1\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"x%5E2%2F49+%2B+%28y-1%29%5E2%2F16+=+1\"$
\n" ); document.write( " \n" ); document.write( "

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