document.write( "Question 826183: Find the equation of the hyperbola that satisfies the given conditions:\r
\n" ); document.write( "\n" ); document.write( " Vertex at (6,5)
\n" ); document.write( " Conjugate axis along x-axis
\n" ); document.write( " Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0 \n" ); document.write( "
Algebra.Com's Answer #497922 by lwsshak3(11628)\"\" \"About 
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Find the equation of the hyperbola that satisfies the given conditions:
\n" ); document.write( "Vertex at (6,5)
\n" ); document.write( "Conjugate axis along x-axis
\n" ); document.write( "Asymptotes 5x - 6y - 30 = 0 and 5x + 6y - 30 = 0
\n" ); document.write( "***
\n" ); document.write( "hyperbola has a vertical transverse axis
\n" ); document.write( "Its standard form of equation: \"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"
\n" ); document.write( "..
\n" ); document.write( "5x-6y-30=0
\n" ); document.write( "6y=5x-30
\n" ); document.write( "y=5x/6-5
\n" ); document.write( "..
\n" ); document.write( "5x+6y-30=0
\n" ); document.write( "6y=-5x+30
\n" ); document.write( "y=-5x/6+5
\n" ); document.write( "slopes of asymptotes=±5/6
\n" ); document.write( "..
\n" ); document.write( "for hyperbolas with a vertical transverse axis, slopes of asymptotes=±a/b=±5/6
\n" ); document.write( "b=±(6/5)a
\n" ); document.write( "a=±5
\n" ); document.write( "a^2=25
\n" ); document.write( "b=±(6/5)a=6
\n" ); document.write( "b^2=36
\n" ); document.write( "..
\n" ); document.write( "asymptotes intersect at center of hyperbola:
\n" ); document.write( "5x-6y-30=0
\n" ); document.write( "5x+6y-30=0
\n" ); document.write( "add:
\n" ); document.write( "10x-60=0
\n" ); document.write( "10x=60
\n" ); document.write( "x=6
\n" ); document.write( "6y=5x-30
\n" ); document.write( "6y=30-30=0
\n" ); document.write( "y=0
\n" ); document.write( "center: (6,0)
\n" ); document.write( "equation of hyperbola:\"y%5E2%2F25-%28x-6%29%5E2%2F36=1\"
\n" ); document.write( ".. \n" ); document.write( "
\n" );