document.write( "Question 963104: Whats the center focus,asymptotes, and vertexes of these 2 equations
\n" ); document.write( " (x-8)^2-(y+6)^2=1
\n" ); document.write( "x^2-y^2=4(x-y)+1 \n" ); document.write( "
Algebra.Com's Answer #588416 by lwsshak3(11628)\"\" \"About 
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Whats the center focus,asymptotes, and vertexes of these 2 equations
\n" ); document.write( "(x-8)^2-(y+6)^2=1
\n" ); document.write( "This is an equation of a hyperbola with 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)=coordinates of center
\n" ); document.write( "For given equation:
\n" ); document.write( "center: (8, -6)
\n" ); document.write( "a^2=1
\n" ); document.write( "a=1
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "vertices: (8±a,-6)=(8±1,-6)=(7,-6) and (9,-6)
\n" ); document.write( "c^2=a^2+b^2=1+1=2
\n" ); document.write( "c=√2≈1.4
\n" ); document.write( "foci: (8±c,-6)=(8±1.4,-6)=(6.6,-6) and (9.4,-6)
\n" ); document.write( "..
\n" ); document.write( "asymptotes: straight lines that go thru center
\n" ); document.write( "form of equation: y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "slope of asymptotes: ±b/a=±1/1=±1
\n" ); document.write( "..
\n" ); document.write( "equation of asymptote with positive slope:
\n" ); document.write( "y=x+b
\n" ); document.write( "solve for b using coordinates of center which are on the line
\n" ); document.write( "-6=1*8+b
\n" ); document.write( "b=-14
\n" ); document.write( "equation: y=x-14
\n" ); document.write( "..
\n" ); document.write( "equation of asymptote with negative slope:
\n" ); document.write( "y=-x+b
\n" ); document.write( "solve for b using coordinates of center which are on the line
\n" ); document.write( "-6=-1*8+b
\n" ); document.write( "b=2
\n" ); document.write( "equation: y=x+2
\n" ); document.write( "..
\n" ); document.write( "x^2-y^2=4(x-y)+1
\n" ); document.write( "x^2-y^2=4x+4y+1
\n" ); document.write( "x^2-4x-y^2-4y=1
\n" ); document.write( "complete the square:
\n" ); document.write( "(x^2-4x+4)-(y^2-4y+4)=1+4+4
\n" ); document.write( "(x-2)^2-(y-2)^2=9
\n" ); document.write( "(x-2)^2/9-(y-2)^2/9=1
\n" ); document.write( "center: (2,2)
\n" ); document.write( "a^2=9
\n" ); document.write( "a=3
\n" ); document.write( "b^2=9
\n" ); document.write( "b=3
\n" ); document.write( "vertices: (2±a,2)=(2±3,2)=(1,2) and (5,2)
\n" ); document.write( "c^2=a^2+b^2=9+9=18
\n" ); document.write( "c=√18≈4.2
\n" ); document.write( "foci: (2±c,2)=(2±4.2,2)=(-2.2,2) and (6.2,2)
\n" ); document.write( "..
\n" ); document.write( "asymptotes: straight lines that go thru center
\n" ); document.write( "form of equation: y=mx+b, m=slope, b=y-intercept
\n" ); document.write( "slope of asymptotes: ±b/a=±9/9=±1
\n" ); document.write( "..
\n" ); document.write( "equation of asymptote with positive slope:
\n" ); document.write( "y=x+b
\n" ); document.write( "solve for b using coordinates of center which are on the line
\n" ); document.write( "2=1*2+b
\n" ); document.write( "b=0
\n" ); document.write( "equation: y=x
\n" ); document.write( "..
\n" ); document.write( "equation of asymptote with negative slope:
\n" ); document.write( "y=-x+b
\n" ); document.write( "solve for b using coordinates of center which are on the line
\n" ); document.write( "2=-1*2+b
\n" ); document.write( "b=4
\n" ); document.write( "equation: y=-x+4 \n" ); document.write( "
\n" );