SOLUTION: Determine the farthest distance from the point (3,7) to the circle x2+y2+4x-6y-12=0

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Question 931562: Determine the farthest distance from the point (3,7) to the circle x2+y2+4x-6y-12=0
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to find the equation of the circle.
x%5E2%2B4x%2By%5E2-6y-12=0
%28x%5E2%2B4x%2B4%29%2B%28y%5E2-6y%2B9%29-12=4%2B9
%28x%2B2%29%5E2%2B%28y-3%29%5E2=25
So the circle is centered at (-2,3) with a radius of 5.
The maximumum distance would be from (3,7) through the center plus the radius of the circle.
First calculate the distance between (3,7) and (-2,3).
D%5E2=%283-%28-2%29%29%5E2%2B%287-3%29%5E2
D%5E2=5%5E2%2B4%5E2
D%5E2=25%2B16
D%5E2=41
D=sqrt%2841%29
So then,
D%5Bmax%5D=D%2B5
D%5Bmax%5D=5%2Bsqrt%2841%29