document.write( "Question 931562: Determine the farthest distance from the point (3,7) to the circle x2+y2+4x-6y-12=0 \n" ); document.write( "

Algebra.Com's Answer #565635 by Fombitz(32388) $\"\"$ $\"About$

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Complete the square to find the equation of the circle.
\n" ); document.write( " $\"x%5E2%2B4x%2By%5E2-6y-12=0\"$
\n" ); document.write( " $\"%28x%5E2%2B4x%2B4%29%2B%28y%5E2-6y%2B9%29-12=4%2B9\"$
\n" ); document.write( " $\"%28x%2B2%29%5E2%2B%28y-3%29%5E2=25\"$
\n" ); document.write( "So the circle is centered at ( $\"-2\"$ , $\"3\"$ ) with a radius of $\"5\"$ .
\n" ); document.write( "The maximumum distance would be from ( $\"3\"$ , $\"7\"$ ) through the center plus the radius of the circle.
\n" ); document.write( "First calculate the distance between ( $\"3\"$ , $\"7\"$ ) and ( $\"-2\"$ , $\"3\"$ ).
\n" ); document.write( " $\"D%5E2=%283-%28-2%29%29%5E2%2B%287-3%29%5E2\"$
\n" ); document.write( " $\"D%5E2=5%5E2%2B4%5E2\"$
\n" ); document.write( " $\"D%5E2=25%2B16\"$
\n" ); document.write( " $\"D%5E2=41\"$
\n" ); document.write( " $\"D=sqrt%2841%29\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"D%5Bmax%5D=D%2B5\"$
\n" ); document.write( " $\"D%5Bmax%5D=5%2Bsqrt%2841%29\"$ \r
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