document.write( "Question 458647: Write an equation for the hyperbola with vertices at (2,5) and (2,1) and a conjugate axis of length 6 units. \n" ); document.write( "

Algebra.Com's Answer #314683 by math-vortex(648) $\"\"$ $\"About$

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A good way to start is to write down the standard form of the equation for a hyperbola. The transverse axis is vertical in this case since it passes through both vertices. (Plot the two vertices on a piece of graph paper if you don’t see why.)\r
\n" ); document.write( "\n" ); document.write( "The standard equation for a hyperbola with a vertical transverse axis is:
\n" ); document.write( " $\"%28y-k%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1\"$ \r
\n" ); document.write( "\n" ); document.write( "The point (h,k) is the center of the hyperbola; it is the midpoint of the line segment between the two vertices at (2,3). This means that h=2 and k=3.
\n" ); document.write( "The parameter a is the distance from the center to each vertex. So, $\"a=2\"$ . (Plot the center on your graph if you don’t see why.)
\n" ); document.write( "The length of the conjugate axis is 2b. We are told that the conjugate axis is 6 units, so b=6/2=3.
\n" ); document.write( "Putting this all together, we have the equation,
\n" ); document.write( " $\"%28y-3%29%5E2%2F2%5E2-%28x-2%29%5E2%2F3%5E2=1\"$
\n" ); document.write( "Simplify:
\n" ); document.write( " $\"%28y-3%29%5E2%2F4-%28x-2%29%5E2%2F9=1\"$
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