document.write( "Question 758896: Determine the equation of the hyperbola whose asymptotes are x±2y=0 and which passes through (4,3) \n" ); document.write( "
Algebra.Com's Answer #461726 by lwsshak3(11628)\"\" \"About 
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Determine the equation of the hyperbola whose asymptotes are x±2y=0 and which passes through (4,3)
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\n" ); document.write( "Hyperbola has a vertical transverse axis since it passes thru (4,3)
\n" ); document.write( "Its standard form of equation: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of center
\n" ); document.write( "Asymptotes are two straight line equations that intersect at center, y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "Equation of asymptote with positive slope:
\n" ); document.write( "x-2y=0
\n" ); document.write( "2y=x
\n" ); document.write( "y=x/2
\n" ); document.write( "m=1/2, b=0
\n" ); document.write( "..
\n" ); document.write( "Equation of asymptote with negative slope:
\n" ); document.write( "x+2y=0
\n" ); document.write( "2y=-x
\n" ); document.write( "y=-x/2
\n" ); document.write( "m=-1/2, b=0
\n" ); document.write( "This means center is at (0,0)
\n" ); document.write( "..
\n" ); document.write( "slopes of asymptotes with vertical transverse axis
\n" ); document.write( "=±a/b=±1/2
\n" ); document.write( "b=±2a
\n" ); document.write( "b^2=4a^2
\n" ); document.write( "..
\n" ); document.write( "solving for a^2 and b^2 using coordinates of given point(4,3)
\n" ); document.write( "(y-k)^2/a^2-(x-h)^2/b^2=1
\n" ); document.write( "y^2/a^2-x^2/4a^2=1
\n" ); document.write( "9/a^2-16/4a^2=1
\n" ); document.write( "9/a^2-4/a^2=1
\n" ); document.write( "5/a^2=1
\n" ); document.write( "a^2=5
\n" ); document.write( "b^2=4a^2=20
\n" ); document.write( "Equation: \"y%5E2%2F5-x%5E2%2F20=1\" \n" ); document.write( "
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