document.write( "Question 578884: solve and graph \"+25x%5E2-16y%5E2-100x-96y-444=0+\" \n" ); document.write( "
Algebra.Com's Answer #370929 by lwsshak3(11628)\"\" \"About 
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solve and graph
\n" ); document.write( "25x^2-16y^2-100x-96y-444=0
\n" ); document.write( "complete the square
\n" ); document.write( "25(x^2-4x+4)-16(y^2+6y+9)=444+100-144=400
\n" ); document.write( "25(x-2)^2-16(y+3)^2=400
\n" ); document.write( "divide by 400=
\n" ); document.write( "(x-2)^2/16-(y+3)^2/25=1
\n" ); document.write( "This equation is that of a hyperbola with horizontal transverse axis of the standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "..
\n" ); document.write( "For given equation:
\n" ); document.write( "center: (2,-3)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=4
\n" ); document.write( "vertices: (2±a,-3)=(2±4,-3)=(-2,-3) and (6,-3)
\n" ); document.write( "..
\n" ); document.write( "b^2=25
\n" ); document.write( "b=5
\n" ); document.write( "length of conjugate axis=2b=10
\n" ); document.write( "..
\n" ); document.write( "slope of asymptotes=±b/a=±5/4
\n" ); document.write( "Asymptotes are straight lines which go thru the center
\n" ); document.write( "Equations for asymptotes:
\n" ); document.write( "y=(5/4)x+b
\n" ); document.write( "solving for b
\n" ); document.write( "-3=(5/4)*2+b
\n" ); document.write( "b=-11/2=-5.5
\n" ); document.write( "equation:
\n" ); document.write( "y=5x/4-5.5
\n" ); document.write( "..
\n" ); document.write( "y=(-5/4)x+b
\n" ); document.write( "solving for b
\n" ); document.write( "-3=(-5/4)*2+b
\n" ); document.write( "b=-.5
\n" ); document.write( "equation:
\n" ); document.write( "y=-5x/4-.5
\n" ); document.write( "..
\n" ); document.write( "See graph below:
\n" ); document.write( "y=±(25(x-2)^2/16-25)^.5-3
\n" ); document.write( " \n" ); document.write( "
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