document.write( "Question 723547: Find the equation of a hyperbola with center at (0,0) and passing through points (-1,-2) and (3,4) \n" ); document.write( "

Algebra.Com's Answer #443351 by lwsshak3(11628) $\"\"$ $\"About$

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Find the equation of a hyperbola with center at (0,0) and passing through points (-1,-2) and (3,4).
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\n" ); document.write( "Standard form of hyperbola with vertical transverse axis with center at origin:
\n" ); document.write( " $\"y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1\"$
\n" ); document.write( "use two given points to set up two equations to solve a and b.
\n" ); document.write( "..
\n" ); document.write( "4/a^2-1/b^2=1
\n" ); document.write( "16/a^2-9/b^2=1
\n" ); document.write( "..
\n" ); document.write( "16/a^2-4/b^2=4
\n" ); document.write( "16/a^2-9/b^2=1
\n" ); document.write( "subtract
\n" ); document.write( "5/b^2=3
\n" ); document.write( "b^2=5/3
\n" ); document.write( "..
\n" ); document.write( "4/a^2-3/5=1
\n" ); document.write( "4/a^2=8/5
\n" ); document.write( "a^2=20/8=5/2
\n" ); document.write( "..
\n" ); document.write( "Equation: $\"y%5E2%2F%285%2F2%29-x%5E2%2F%285%2F3%29=1\"$
\n" ); document.write( "This is an equation of a hyperbola with vertical transverse axis.
\n" ); document.write( "note: I tried with a horizontal transverse axis at first but that did not come out right. \n" ); document.write( "

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