document.write( "Question 451835: what is the standard form of x^2-4x-4y^2+8y-100=0 \n" ); document.write( "
Algebra.Com's Answer #310805 by lwsshak3(11628)\"\" \"About 
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what is the standard form of x^2-4x-4y^2+8y-100=0
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\n" ); document.write( "Completing the square is the first for finding out what kind of conic this equation is:
\n" ); document.write( "(x^2-4x+4)-4(y^2-2y+1)=100
\n" ); document.write( "(x-2)^2-4(y-1)^2=100+4-4=100
\n" ); document.write( "divide by 100
\n" ); document.write( "(x-2)^2/100-(y-1)^2/25=1
\n" ); document.write( "Standard form of a hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "Standard form of a hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1, with (h,k) being the (x,y) coordinates of the center.
\n" ); document.write( "Note that the only difference between the two forms is the interchange of (y-k)^2 with (x-h)^2.
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\n" ); document.write( "Given hyperbola is of the first form with a horizontal transverse axis (hyperbola opens sideways) and center at (2,1).
\n" ); document.write( "a^2=100
\n" ); document.write( "a=10
\n" ); document.write( "length of transverse axis=2a=20
\n" ); document.write( "b^2=25
\n" ); document.write( "b=5
\n" ); document.write( "Length of conjugate axis=2b=10 \n" ); document.write( "
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