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find the center, the vertices, foci, and the asymptotes of the hyperbola. then draw the graph.
\n" ); document.write( "x^2-y^2+4x+6y-6=0
\n" ); document.write( "**
\n" ); document.write( "x^2-y^2+4x+6y-6=0
\n" ); document.write( "completing the squares:
\n" ); document.write( "(x^2+4x+4)-(y^2-6y+9)-6-4+9=0
\n" ); document.write( "(x+2)^2-(y-3)^2=1
\n" ); document.write( "This is an equation of a hyperbola with horizontal transverse axis of the standard form:
\n" ); document.write( "(x-h)^2/a^2-(y-k)^2=1
\n" ); document.write( "..
\n" ); document.write( "For given equation:
\n" ); document.write( "center:(-2,3)
\n" ); document.write( "a^2=1
\n" ); document.write( "a=1
\n" ); document.write( "length of transverse axis=2a=2
\n" ); document.write( "vertices: (-2±a,3) =(-2±1,3) or (-3,3) and (-1,3)
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "c^2=a^2+b^2=1+1=2
\n" ); document.write( "c=√2
\n" ); document.write( "Foci: (-2±c,3)=(-2±√2,3) or (-2-√2,3) and (-2+√2,3)
\n" ); document.write( "..
\n" ); document.write( "Asymptotes:
\n" ); document.write( "slope,m=±b/a=±1/1=±1
\n" ); document.write( "Equations:
\n" ); document.write( "y=±x+b
\n" ); document.write( "finding b using (x,y) coordinates of center (-2,3)
\n" ); document.write( "3=-2=b
\n" ); document.write( "b=5
\n" ); document.write( "equation: y=x+5
\n" ); document.write( "..
\n" ); document.write( "y=-x+b
\n" ); document.write( "3=-(-2)+b
\n" ); document.write( "b=1
\n" ); document.write( "equation: y=-x+1
\n" ); document.write( "..
\n" ); document.write( "center:(-2,3)
\n" ); document.write( "vertices: (-3,3) and (-1,3)
\n" ); document.write( "Foci: (-2-√2,3) and (-2+√2,3)
\n" ); document.write( "Asymptotes:y=x+5 and y=-x+1\r
\n" ); document.write( "\n" ); document.write( "see graph below as a visual check on answers:
\n" ); document.write( "..
\n" ); document.write( "y=±((x+2)^2-1)^.5+3
\n" ); document.write( "