SOLUTION: find the radius of the circle defined by the equation: x^2+y^2+12x+4y+76=0.

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Question 372701: find the radius of the circle defined by the equation: x^2+y^2+12x+4y+76=0.
Found 2 solutions by Fombitz, ewatrrr:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square in x and y.
x%5E2%2By%5E2%2B12x%2B4y%2B76=0
%28x%5E2%2B12x%2B36%29%2B%28y%5E2%2B4y%2B4%29%2B76=36%2B4
%28x%2B6%29%5E2%2B%28y%2B2%29%5E2=40-76
%28x%2B6%29%5E2%2B%28y%2B2%29%5E2=-36
Compare this equation to the general equation of a circle centered at (h,k) with a radius R.
%28x-h%29%5E2%2B%28y-k%29%5E2=R%5E2
In this case, your equation is not the equation for a circle.


Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

The standard equation of a circle with center C(h,k) and radius r is :

%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2

Find the radius  

x^2+y^2+12x+4y+76=0

completing the squares

x^2+12x +   y^2+4y       + 76=0

(x+6)^2 + (y+2)^2 -36 -4 + 76 = 0

(x+6)^2 + (y+2)^2 = 36 = 6^2

radius = 6, center (-6,-2)