document.write( "Question 316948: Write the equation of the circle containing the points J(-6, 0), K(-3, 3), and L(0, 0). Show all work to receive credit \n" ); document.write( "

Algebra.Com's Answer #226902 by Fombitz(32388) $\"\"$ $\"About$

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The general equation for a circle centered at (h,k) with a radius R is:
\n" ); document.write( " $\"%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2\"$
\n" ); document.write( "or more usefully,
\n" ); document.write( " $\"%28h-x%29%5E2%2B%28y-k%29%5E2=R%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "J: $\"%28h%2B6%29%5E2%2B%28k-0%29%5E2=R%5E2\"$
\n" ); document.write( "K: $\"%28h%2B3%29%5E2%2B%28k-3%29%5E2=R%5E2\"$
\n" ); document.write( "L: $\"%28h-0%29%5E2%2B%28k-0%29%5E2=R%5E2\"$
\n" ); document.write( "From the L equation,
\n" ); document.write( " $\"h%5E2%2Bk%5E2=R%5E2\"$
\n" ); document.write( "From the J equation,
\n" ); document.write( " $\"%28h%2B6%29%5E2%2Bk%5E2=R%5E2\"$
\n" ); document.write( "Equate those two,
\n" ); document.write( " $\"h%5E2%2Bk%5E2=%28h%2B6%29%5E2%2Bk%5E2\"$
\n" ); document.write( " $\"h%5E2=%28h%2B6%29%5E2\"$
\n" ); document.write( " $\"h%5E2=h%5E2%2B12h%2B36\"$
\n" ); document.write( " $\"12h%2B36=0\"$
\n" ); document.write( " $\"highlight%28h=-3%29\"$
\n" ); document.write( "From the K equation,
\n" ); document.write( " $\"%28k-3%29%5E2=R%5E2\"$
\n" ); document.write( "From the L equation,
\n" ); document.write( " $\"9%2Bk%5E2=R%5E2\"$
\n" ); document.write( "Equate those two,
\n" ); document.write( " $\"9%2Bk%5E2=k%5E2-6k%2B9\"$
\n" ); document.write( " $\"-6k=0\"$
\n" ); document.write( " $\"highlight%28k=0%29\"$
\n" ); document.write( "Finally using L,
\n" ); document.write( " $\"9%2B0=R%5E2\"$
\n" ); document.write( " $\"highlight%28R%5E2=9%29\"$
\n" ); document.write( ".
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\n" ); document.write( " $\"highlight_green%28%28x%2B3%29%5E2%2By%5E2=9%29\"$ \n" ); document.write( "

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