document.write( "Question 812335: The foci of a hyperbola are F1(-20,0) and F2(20,0). The difference between the distances from any point, P(x,y), on the hyperbola, to its foci, is 24. Determine the equation of the hyperbola. \n" ); document.write( "

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The foci of a hyperbola are F1(-20,0) and F2(20,0). The difference between the distances from any point, P(x,y), on the hyperbola, to its foci, is 24. Determine the equation of the hyperbola.
\n" ); document.write( "***
\n" ); document.write( "Hyperbola has a horizontal transverse axis.
\n" ); document.write( "Its standard form of equation: $\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"$ , (h,k) =(x,y) coordinates of center.
\n" ); document.write( "center: (0,0)
\n" ); document.write( "2a=24
\n" ); document.write( "a=12
\n" ); document.write( "a^2=144
\n" ); document.write( "c=20(distance from center to foci)
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "b^2=c^2-a^2=400-144=256
\n" ); document.write( "b^2=256
\n" ); document.write( "b=√256=16
\n" ); document.write( "Equation:
\n" ); document.write( " $\"x%5E2%2F144-y%5E2%2F256=1\"$
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