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Graph the hyperbola given by the equation 4x^2+8x-y^2-2y-1=0.
\n" ); document.write( "**
\n" ); document.write( "4x^2+8x-y^2-2y-1=0
\n" ); document.write( "completing the squares:
\n" ); document.write( "4(x^2+2x+1)-(y^2+2y+1)=1+4-1=4
\n" ); document.write( "4(x+1)^2-(y+1)^2=4
\n" ); document.write( "(x+1)^2/1-(y+1)^2/4=1
\n" ); document.write( "This is a hyperbola with horizontal transverse axis. (opens sideways)
\n" ); document.write( "Standard form: (x-h)^2/a^2-(y-k)^2/b^2=1
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-1,-1)
\n" ); document.write( "a^2=1
\n" ); document.write( "a=1
\n" ); document.write( "length of transverse axis=2a=2
\n" ); document.write( "Vertices: (-1±a,-1)=(-1±1,-1)
\n" ); document.write( "..
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "length of conjugate axis=2b=4
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2+b^2=1+4=5
\n" ); document.write( "c√5=2.24
\n" ); document.write( "Foci: (-1±√5,-1)
\n" ); document.write( "..
\n" ); document.write( "Two Asymptotes:y=±mx+b
\n" ); document.write( "y=mx+b
\n" ); document.write( "m=b/a=2/1=2
\n" ); document.write( "Solving for b using (x,y) coordinates of center
\n" ); document.write( "-1=2(-1)+b
\n" ); document.write( "b=1
\n" ); document.write( "y=2x+1
\n" ); document.write( "..
\n" ); document.write( "y=-mx+b
\n" ); document.write( "-1=-2(-1)+b
\n" ); document.write( "b=-3
\n" ); document.write( "y=-2x-3
\n" ); document.write( "see graph as a visual check on answers above\r
\n" ); document.write( "\n" ); document.write( "..
\n" ); document.write( "y=±(-4+4(x+1)^2)^.5-1
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