document.write( "Question 725832: what is the equation of a hyperbola centered on the origin with asymptotic lines of y=2x and y=-2x and a known vertex at (0,4)? \n" ); document.write( "

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what is the equation of a hyperbola centered on the origin with asymptotic lines of y=2x and y=-2x and a known vertex at (0,4)?
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\n" ); document.write( "This is a hyperbola with vertical transverse axis.
\n" ); document.write( "Its standard form of equation: $\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of center
\n" ); document.write( "a=4(distance from center to vertex)
\n" ); document.write( "a^2=16
\n" ); document.write( "..
\n" ); document.write( "For hyperbolas with vertical transverse axis, slope of asymptotes=a/b=ą2
\n" ); document.write( "a^2/b^2=4
\n" ); document.write( "b^2=a^2/4=16/4=4
\n" ); document.write( "...
\n" ); document.write( "Equation of given hyperbola:
\n" ); document.write( " $\"y%5E2%2F16-x%5E2%2F4=1\"$ \n" ); document.write( "

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