SOLUTION: Given this equation find the radius and center of a circle. {{{x^2+6x+y^2-5y=-1/4}}}

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Question 16112: Given this equation find the radius and center of a circle. x%5E2%2B6x%2By%5E2-5y=-1%2F4
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You want to get your equation into the standard form for a circle with center at (h, k) and radius r. It will look like this:
%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2
To do this, you must:
1) Complete the square in the x-terms.
2) Complete the square in the y-terms.
3) Factor the resulting x-trinomial.
4) Factor the resulting y-trinomial.
5) Simplify, if necessary, into the standard form.
%28x%5E2+%2B+6x%29+%2B+%28y%5E2+-+5y%29+=+-1%2F4 Complete the squares by adding the square of half the coefficient of x/y to both sides.
%28x%5E2+%2B+6x+%2B+9%29+%2B+%28y%5E2+-+5y+%2B+25%2F4%29+=+-1%2F4+%2B+9+%2B+25%2F4 Factor the x and the y trinomials and simplify the right side of the equation.
%28x+%2B+3%29%5E2+%2B+%28y+-+5%2F2%29%5E2+=+15 Compare this with the standard form. %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2
The center of the circle is at (-3, 5/2) and the radius is sqrt%2815%29