document.write( "Question 619252: Whats the standard form of an ellipse with verticies at (-5,-6) and (-5,8) and a minor axis of 6? \n" ); document.write( "
Algebra.Com's Answer #389543 by KMST(5328)\"\" \"About 
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STEP 1 - FIND THE DIRECTION OF THE MAJOR AXIS:
\n" ); document.write( "The major axis extends between the vertices, and since the vertices have the same x-coordinate (x=-5), the major axis is vertical (parallel to the y-axis), along the line x=-5.
\n" ); document.write( "On that line, we find the vertices, the foci, and the center.
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\n" ); document.write( "STEP 2 - FIND THE CENTER:
\n" ); document.write( "The center is midway between the vertices, so we average the coordinates of the vertices to find the midpoint of the segment (the major axis) that connects those vertices.
\n" ); document.write( "We already know that the x-coordinate is -5.
\n" ); document.write( "We just need to average the y-coordinates of the vertices.
\n" ); document.write( "The center will be (-5,\"%28-6%2B8%29%2F2\")=(-5,1)
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\n" ); document.write( "STEP 3 - FIND THE SEMI-MAJOR AXIS:
\n" ); document.write( "The semi-major axis is called a, and is the distance from the center to a vertex.
\n" ); document.write( "It's \"a=8-1=7\"
\n" ); document.write( "(It could also be calculated as half the distance between the vertices).
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\n" ); document.write( "STEP 4 - FIND THE SEMI-MINOR AXIS:
\n" ); document.write( "The minor axis is the distance between the co-vertices, and the problem says it's 6.
\n" ); document.write( "The semi-minor axis is called b, and is half of the minor axis, so b=3.
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\n" ); document.write( "STEP 5 - WRITE THE EQUATION:
\n" ); document.write( "The equation involves the coordinates of the center (x=-5, y=1), subtracted from x and y, and then squared:
\n" ); document.write( "\"%28x-%28-5%29%29%5E2=%28x%2B5%29%5E2\" and \"%28y-1%29%5E2\"
\n" ); document.write( "Those squares are divided by \"a%5E2=7%5E2\" and \"b%5E2=3%5E2\".
\n" ); document.write( "Since the major axis extends vertically, the \"a%5E2\" will be dividing the \"%28y-1%29%5E2\".
\n" ); document.write( "The equation is
\n" ); document.write( "\"highlight%28%28x%2B5%29%5E2%2F3%5E2%2B%28y-1%29%5E2%2F7%5E2=1%29\" or \"highlight%28%28x%2B5%29%5E2%2F9%2B%28y-1%29%5E2%2F49=1%29\"
\n" ); document.write( "It shows that from the center (-5,1), the ellipse extends horizontally 3 units to the left and to the right, to co-vertices with y=1, such that
\n" ); document.write( "\"%28x%2B5%29%5E2%2F3%5E2=1\" or \"%28x%2B5%29%5E2=3%5E2\" or \"%28x-%28-5%29%29%5E2=3%5E2\" , and
\n" ); document.write( "that it extends vertically 7 units up and down from the center to vertices with x=-5, and such that
\n" ); document.write( "\"%28y-1%29%5E2%2F7%5E2=1\" or \"%28y-1%29%5E2=7%5E2\" \n" ); document.write( "
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