document.write( "Question 1026719: The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle? \n" ); document.write( "
Algebra.Com's Answer #641988 by mathmate(429)\"\" \"About 
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\n" ); document.write( "Question:
\n" ); document.write( "The equation x^2+y^2-2x-4y-4=0 represents a circle. What are the coordinates for the center of the circle? What is the length of the radius of the circle?
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\n" ); document.write( "Solution:
\n" ); document.write( "The general equation of a circle centred at (a,b) with radius r is written as:
\n" ); document.write( "\"%28x-a%29%5E2%2B%28y-b%29%5E2=r%5E2\"........ (1)
\n" ); document.write( "By completing squares, we have
\n" ); document.write( "\"x%5E2%2By%5E2-2x-4y-4\"
\n" ); document.write( "=\"x%5E2-2x%2B1-1+%2B+y%5E2-4y%2B4-4+-4\"
\n" ); document.write( "=\"%28x-1%29%5E2+-1+%2B+%28y-2%29%5E2+-4+-4+\"
\n" ); document.write( "=\"%28x-1%29%5E2%2B%28y-2%29%5E2-9\"
\n" ); document.write( "=0
\n" ); document.write( "Hence the equation of the circle can be rewritten as
\n" ); document.write( "(x-1)^2+(y-2)^2=3^3
\n" ); document.write( "By comparison with the general equation (1) above, we conclude that the centre of the circle is (a,b)=(1,2) and the radius is 3.
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