document.write( "Question 751431: find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4) \n" ); document.write( "

Algebra.Com's Answer #457198 by lwsshak3(11628) $\"\"$ $\"About$

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find and equation for a hyperbola with vertices at (2,3) and (2,-1) and foci at (2,6) and (2,-4)
\n" ); document.write( "hyperbola has a vertical transverse axis.
\n" ); document.write( "Its standard form of equation: $\"%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of the center
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "x-coordinate of center=2
\n" ); document.write( "y-coordinate of center=1 (midpoint of vertical transverse axis)
\n" ); document.write( "center: (2,1)
\n" ); document.write( "a=2 (distance from center to vertices)
\n" ); document.write( "a^2=4
\n" ); document.write( "c=5 (distance from center to foci)
\n" ); document.write( "c^2=25
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "b^2=c^2-a^2=25-4=21
\n" ); document.write( "Equation of given hyperbola:
\n" ); document.write( " $\"%28y-1%29%5E2%2F4-%28x-2%29%5E2%2F21=1\"$ \n" ); document.write( "

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