document.write( "Question 1165933: Endpoints of major axis at (−4, 2) and (12, 2); endpoints of the minor axis at (4, 4) and (4, 0) . finding the general form \n" ); document.write( "

Algebra.Com's Answer #790445 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Don't use special characters in your posts. Fortunately, it is obvious from the rest of the given information that the first endpoint of the major axis is (-4,2).

\n" ); document.write( "This is an ellipse with horizontal major axis; the general form is

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

\n" ); document.write( "(h,k) is the center; a is the semi-major axis; b is the semi-minor axis.

\n" ); document.write( "The length of the major axis is 16 (from (-4,2) to (12,2)), so the semi-major axis is 8.

\n" ); document.write( "The length of the minor axis is 4 (from (4,4) to (4,0)), so the semi-minor axis is 2.

\n" ); document.write( "To find the center (h,k), you can use the midpoint of either the major or minor axis; those midpoints are (4,2).

\n" ); document.write( "Note you can also find the center by noting that the major axis is on the line y=2 and the minor axis is on the line x=4 -- making the intersection of the axes at (4,2).

\n" ); document.write( "So we have (h,k) = (4,2); a=8; b=2.

\n" ); document.write( "So the equation is

\n" ); document.write( " $\"%28x-4%29%5E2%2F64%2B%28y-2%29%5E2%2F4=1\"$

\n" ); document.write( " \n" ); document.write( "

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