document.write( "Question 765278: i need help finding the center, vertices, and foci of this equation 9x^2+36(y-2)^2-324=0 \n" ); document.write( "

Algebra.Com's Answer #466058 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"9x%5E2%2B36%28y-2%29%5E2-324=0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2B36%28y-2%29%5E2=324\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9x%5E2%2F324%2B36%28y-2%29%5E2%2F324=324%2F324\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cross%289%29x%5E2%2Fcross%28324%2936%2Bcross%2836%29%28y-2%29%5E2%2Fcross%28324%299=1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2F36%2B%28y-2%29%5E2%2F9=1\"$ or\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-0%29%5E2%2F36%2B%28y-2%29%5E2%2F9=1\"$ \r
\n" ); document.write( "\n" ); document.write( "this is an ellipse with $\"h=0\"$ and $\"k=2\"$ ; so, the center is at\r
\n" ); document.write( "\n" ); document.write( "( $\"0\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "we also know that semi-major axis $\"a=6\"$ and semi-minor axis $\"b=3\"$ ; so, we have an ellipse with horizontal major axis\r
\n" ); document.write( "\n" ); document.write( "vertices:
\n" ); document.write( "( $\"h-a\"$ , $\"k\"$ ) =>( $\"0-6\"$ , $\"2\"$ )=>( $\"-6\"$ , $\"2\"$ )
\n" ); document.write( "( $\"h%2Ba\"$ , $\"k\"$ )=>( $\"0%2B6\"$ , $\"2\"$ )=>( $\"6\"$ , $\"2\"$ )\r
\n" ); document.write( "\n" ); document.write( "c0-vertices:
\n" ); document.write( "( $\"k\"$ , $\"k-b\"$ ) =>( $\"2\"$ , $\"2-3\"$ )=>( $\"2\"$ , $\"-1\"$ )
\n" ); document.write( "( $\"k\"$ , $\"k%2Bb\"$ )=>( $\"2\"$ , $\"2%2B3\"$ )=>( $\"2\"$ , $\"5\"$ )\r
\n" ); document.write( "\n" ); document.write( "foci:\r
\n" ); document.write( "\n" ); document.write( "The formula generally associated with the focus of an ellipse is\r
\n" ); document.write( "\n" ); document.write( " $\"+c%5E2=+a%5E2+-+b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"b=3\"$ and $\"a=6\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c%5E2=+6%5E2+-+3%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c%5E2=36+-+9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c%5E2=27\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c=sqrt%2827%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c=5.19\"$ and $\"+c=-5.19\"$ \r
\n" ); document.write( "\n" ); document.write( "so, foci is at ( $\"5.19\"$ , $\"2\"$ ) and ( $\"-5.19\"$ , $\"2\"$ )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

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

\n" );