document.write( "Question 968306: Find the coordinates of the center of a circle containing the points (0,0), (-2,4) and (4,-2) \n" ); document.write( "

Algebra.Com's Answer #591722 by lwsshak3(11628) $\"\"$ $\"About$

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Find the coordinates of the center of a circle containing the points (0,0), (-2,4) and (4,-2)
\n" ); document.write( "***
\n" ); document.write( "standard form of equation for a circle: (x-h)^2+(y-k)^2=r^2, (h,k)=coordinates of center, r=radius
\n" ); document.write( "..
\n" ); document.write( "(0,0) (0-h)^2+(0-k)^2=r^2
\n" ); document.write( "h^2+k^2=r^2
\n" ); document.write( "..
\n" ); document.write( "(-2,4) (-2-h)^2+(4-k)^2=r^2
\n" ); document.write( "4+4h+h^2+16-8k+k^2=r^2
\n" ); document.write( "4+4h+h^2+16-8k+k^2=h^2+k^2 (sub (h^2+k^2) for r^2)
\n" ); document.write( "4+4h+16-8k=0
\n" ); document.write( "4h-8k=-20
\n" ); document.write( "..
\n" ); document.write( "(4,-2) (4-h)^2+(-2-k)^2=r^2
\n" ); document.write( "16-8h+h^2+4+4k+k^2=r^2
\n" ); document.write( "16-8h+h^2+4+4k+k^2=h^2+k^2 (sub (h^2+k^2) for r^2)
\n" ); document.write( "16-8h+4+4k=0
\n" ); document.write( "-8h+4k=-20
\n" ); document.write( "..
\n" ); document.write( "4h-8k=-20
\n" ); document.write( "-8h+4k=-20
\n" ); document.write( "..
\n" ); document.write( "8h-16k=-40(mult. eq. by 2)
\n" ); document.write( "-8h+4k=-20
\n" ); document.write( "add:
\n" ); document.write( "-12k=-60
\n" ); document.write( "k=5
\n" ); document.write( "..
\n" ); document.write( "4h=-20+8k=-20+40
\n" ); document.write( "4h=20
\n" ); document.write( "h=5
\n" ); document.write( "r^2=h^2+k^2=25+25=50
\n" ); document.write( "..
\n" ); document.write( "equation: (x-5)^2+(y-5)^2=50
\n" ); document.write( "center:(5, 5) \n" ); document.write( "

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