document.write( "Question 113439: Write the equation of a hyperbola that passes through the point at (4,2) and has asymptotes with equations y=2x and y=-2x+4.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #82622 by scott8148(6628) $\"\"$ $\"About$

You can put this solution on YOUR website!
the center of the hyperbola (h,k) is the intersection of the asymptotes, (1,2)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the parabola passes through (4,2) which is directly above the center
\n" ); document.write( "___ this means an East-West opening parabola of the form $\"%28%28%28x-h%29%5E2%29%2Fa%5E2%29-%28%28%28y-k%29%5E2%29%2Fb%5E2%29=1\"$
\n" ); document.write( "___ the slope of the asymptotes is ą(b/a), so b=2a and b^2=4a^2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "(((4-1)^2)/(a^2))-(((2-2)^2)/(4a^2))=1 ___ ((3^2)/(a^2))-0=1 ___ 3^2=a^2 ___ 3=a ___ so b=6\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28%28%28x-1%29%5E2%29%2F9%29-%28%28%28y-2%29%5E2%29%2F36%29=1\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );