document.write( "Question 1048583: Please help me answer this question?\r
\n" ); document.write( "\n" ); document.write( "Find an equation for the ellipse that satisfies the given conditions:\r
\n" ); document.write( "\n" ); document.write( "Foci (1, ą4), vertices (1, ą7) \n" ); document.write( "

Algebra.Com's Answer #664195 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Find an equation for the ellipse that satisfies the given conditions:
\n" ); document.write( "Foci (1, ą4),
\n" ); document.write( "vertices (1, ą7) \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The center is midway between the two foci, so ( $\"h\"$ , $\"+k\"$ ) = ( $\"1\"$ , $\"0\"$ ), by the Midpoint Formula.
\n" ); document.write( "Each focus is $\"4\"$ units from the center, so $\"c+=+4\"$ . \r
\n" ); document.write( "\n" ); document.write( "The vertices are $\"7\"$ units from the center, so $\"a+=+7\"$ .
\n" ); document.write( "Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide. Then $\"a%5E2\"$ will go with the $\"y\"$ part of the equation.\r
\n" ); document.write( "\n" ); document.write( " $\"%28y-k%29%5E2%2Fa%5E2%2B%28x-h%29%5E2%2Fb%5E2+=+1\"$ \r
\n" ); document.write( "\n" ); document.write( "The equation $\"b%5E2+=+a%5E2+-+c%5E2\"$ gives me
\n" ); document.write( " $\"b%5E2+=+7%5E2+-+4%5E2\"$ ,
\n" ); document.write( " $\"b%5E2+=+49+-+16\"$
\n" ); document.write( " $\"b%5E2+=+33\"$
\n" ); document.write( "and this is all I need to create my equation:\r
\n" ); document.write( "\n" ); document.write( " $\"+%28y+-+0%29%5E2+%2F+49+%2B+%28x-1%29%5E2+%2F+33=+1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+%5E2+%2F+49+%2B+%28x-1%29%5E2+%2F+33=+1\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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