document.write( "Question 495972: I know that the following equation will result in a circle graph (the teacher's key says so). But I would like to know how to get there. I need to isolate y:\r
\n" ); document.write( "\n" ); document.write( "x^2 + y^2 - 4y = 21
\n" ); document.write( "(that is, x squared plus y squared minus 4y equals 21)\r
\n" ); document.write( "\n" ); document.write( "Thank you
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Algebra.Com's Answer #336276 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
general form of a circle:
\n" ); document.write( "(x - h)^2 + (y - k)^2 = r^2
\n" ); document.write( ".
\n" ); document.write( "your equation:
\n" ); document.write( "x^2 + y^2 - 4y = 21
\n" ); document.write( "subtracting x^2 from both sides:
\n" ); document.write( "y^2 - 4y = -x^2 + 21
\n" ); document.write( "\"complete the square\" by adding 2 to both sides:
\n" ); document.write( "y^2 - 4y + 2 = -x^2 + 21 + 2
\n" ); document.write( "(y-2)(y-2) = -x^2 + 23
\n" ); document.write( "(y-2)^2 = -x^2 + 23
\n" ); document.write( "add x^2 to both sides:
\n" ); document.write( "x^2 + (y-2)^2 = 23 (equation of the circle)
\n" ); document.write( ".
\n" ); document.write( "Or, you can think of it as:
\n" ); document.write( "(x-0)^2 + (y-2)^2 = 23
\n" ); document.write( "Now, we can see the center is at (0,2)
\n" ); document.write( "with a radius of square root of 23\r
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