document.write( "Question 1087740: Please help me solve this hyperbola equation with vertices(5,-3) and (-1,-3) and afocus at (7,-3) \n" ); document.write( "

Algebra.Com's Answer #702040 by MathLover1(20850) $\"\"$ $\"About$

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hyperbola equation with vertices ( $\"5\"$ , $\"-3\"$ ) and ( $\"-1\"$ , $\"-3\"$ ) and a focus at ( $\"7\"$ , $\"-3\"$ ) \r
\n" ); document.write( "\n" ); document.write( "the standard form of the equation is: looking at coordinates of vertices, yu have a horizontal hyperbola\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "center: ( $\"h\"$ , $\"k\"$ )
\n" ); document.write( "vertices: ( $\"h\"$ ą $\"a\"$ , $\"+k\"$ )
\n" ); document.write( "foci: ( $\"h\"$ ą $\"c\"$ , $\"k\"$ ) \r
\n" ); document.write( "\n" ); document.write( "The vertices are above and below each other, so the center, foci, and vertices lie on a vertical line paralleling the y-axis\r
\n" ); document.write( "\n" ); document.write( "The center is $\"midway\"$ between the two vertices, so if vertices at ( $\"5\"$ , $\"-3\"$ ) and ( $\"-1\"$ , $\"-3\"$ )
\n" ); document.write( " ( $\"h\"$ , $\"+k\"$ )=( $\"%285%2B%28-1%29%29%2F2\"$ , $\"%28-3%2B%28-3%29%29%2F2\"$ )=( $\"2\"$ , $\"-3\"$ )\r
\n" ); document.write( "\n" ); document.write( "so, $\"h=2\"$ \r
\n" ); document.write( "\n" ); document.write( "since vertices:
\n" ); document.write( " ( $\"h\"$ ą $\"+a\"$ , $\"k\"$ ) =( $\"5\"$ , $\"-3\"$ )=>
\n" ); document.write( " $\"h\"$ ą $\"a\"$ = $\"5\"$ and since $\"k=-3\"$ and $\"h=2\"$ we can find $\"a\"$ \r
\n" ); document.write( "\n" ); document.write( "so,
\n" ); document.write( " $\"2%2Ba=5\"$
\n" ); document.write( " $\"a=5-2\"$
\n" ); document.write( " $\"a=3\"$ \r
\n" ); document.write( "\n" ); document.write( "since foci:
\n" ); document.write( "( $\"h\"$ ą $\"c\"$ , $\"k\"$ )=( $\"7\"$ , $\"-3\"$ ) =>
\n" ); document.write( " $\"h+%2Bc=7\"$ and since $\"h=2\"$ we have
\n" ); document.write( " $\"c=7-2\"$
\n" ); document.write( " $\"c=5\"$ \r
\n" ); document.write( "\n" ); document.write( "since $\"+c=sqrt%28a%5E2+%2B+b%5E2%29\"$ we can find $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"5=sqrt%283%5E2+%2B+b%5E2%29\"$
\n" ); document.write( "
\n" ); document.write( " $\"25=9+%2B+b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b%5E2=25-9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b%5E2=16\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=4\"$ or $\"b=-4\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your equation is:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-2%29%5E2%2F3%5E2-%28y%2B3%29%5E2%2F4%5E2=1\"$ \r
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