document.write( "Question 390094: how do I graph these two equations ? (x^2-12x+84=y^2+16y) , (x^2+y^2=4x+9) ? (ie, simplify, get center/radius) \n" ); document.write( "
Algebra.Com's Answer #278316 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
If you want to simply graph these two equations, solve for y then plot it manually or on a graphing calculator.\r
\n" ); document.write( "\n" ); document.write( "given: x^2-12x+84=y^2+16y
\n" ); document.write( "complete the square
\n" ); document.write( "x^2-12x+36-( y^2+16x+64)=-84+36-64=-112
\n" ); document.write( "(x-6)^2-(y+8)^2=-112
\n" ); document.write( "multiply by (-1)
\n" ); document.write( "(y+8)^2-(x-6)^2=112
\n" ); document.write( "(y+8)^2/112 + (x-6)^2/112 = 1
\n" ); document.write( "This is a hyperbola with center at (6,-8), and transverse axis in the vertical direction.\r
\n" ); document.write( "\n" ); document.write( "solving for y
\n" ); document.write( "(y+8)^2 = 112+(x-6)^2 = 112+x^2-12x+36
\n" ); document.write( "y+8 =sqrt( 112+x^2-12x+36) =( 112+x^2-12x+36)^.5
\n" ); document.write( "y=-8+( 112+x^2-12x+36)^.5, and -8-( 112+x^2-12x+36)^.5
\n" ); document.write( "The first expression will graph the top half of the hyperbola and the second, the bottom half\r
\n" ); document.write( "\n" ); document.write( "Now, for the other given equation, x^2+y^2=4x+9
\n" ); document.write( "complete the square
\n" ); document.write( "x^2-4x+4+y^2 = 9+4=13
\n" ); document.write( "(x-2)^2+y^2 = 13
\n" ); document.write( "This is a circle with center at (2,0) with radius sqrt(13)
\n" ); document.write( "solving for y
\n" ); document.write( "y^2 = 13-(x-2)^2=13-x^2+4x-4
\n" ); document.write( "y = ħsqrt(13-x^2+4x-4) or ħ(13-x^2+4x-4)^.5
\n" ); document.write( "The first (+)expression will graph the top half of the circle and the second(-), the bottom half
\n" ); document.write( "The following graph will give you some idea what the curves look like.
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