document.write( "Question 697821: if x+y^2+kxy+8x-6y+9=0 represents a circle state the value of k and substituting this value of k in the equation;find the center and radius of the circle \n" ); document.write( "

Algebra.Com's Answer #430899 by KMST(5328) $\"\"$ $\"About$

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It should have a term with $\"x%5E2\"$ .
\n" ); document.write( "If $\"x%5E2%2By%5E2%2Bkxy%2B8x-6y%2B9=0\"$ represents a circle,
\n" ); document.write( " $\"k=0\"$ .
\n" ); document.write( "(Terms in $\"xy\"$ appear when a conic section other than a circle has axes that are not parallel to the x- and y-axes, but circles do not care about rotating the axes).
\n" ); document.write( "
\n" ); document.write( " $\"x%5E2%2By%5E2%2B8x-6y%2B9=0\"$ --> $\"%28x%5E2%2B8x%29%2B%28y%5E2-6y%29=-9\"$ --> $\"%28x%5E2%2B8x%2B16%29%2B%28y%5E2-6y%2B9%29=-9%2B16%2B9\"$ --> $\"%28x%2B4%29%5E2%2B%28x-3%29%5E2=16\"$ --> $\"%28x%2B4%29%5E2%2B%28x-3%29%5E2=4%5E2\"$
\n" ); document.write( "The last equation shows that the circle is centered at the point (-4,3),
\n" ); document.write( "because $\"x%5BC%5D=-4\"$ and $\"y%5BC%5D=3\"$ are the coordinates of the center, subtracted from $\"x\"$ and $\"y\"$ in the equation.
\n" ); document.write( "It also shows that the radius is $\"4\"$ . \n" ); document.write( "

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