SOLUTION: Please help me: It says to Complete the square to find the center of the radius of the given circle.Could you show me the steps in completing this. A{{{x^2+y^2+6x-4y-3=0}}} B

Algebra ->  Algebra  -> Circles -> SOLUTION: Please help me: It says to Complete the square to find the center of the radius of the given circle.Could you show me the steps in completing this. A{{{x^2+y^2+6x-4y-3=0}}} B      Log On

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Question 94328: Please help me: It says to Complete the square to find the center of the radius of the given circle.Could you show me the steps in completing this.
Ax%5E2%2By%5E2%2B6x-4y-3=0
B 2x%5E2%2B2y%5E2-4x%2B8y-24=0
Thank you
Answer by Earlsdon(6098) About Me  (Show Source):
You can put this solution on YOUR website!
A. Complete the square to find the centre and the radius.
x%5E2%2By%5E2%2B6x-4y-3+=+0 Add 3 to both sides.
x%5E2%2By%5E2%2B6x-4y+=+3 Group the like-terms together on the left side.
%28x%5E2%2B6x%29+%2B+%28y%5E2-4y%29+=+3 Now complete the squares in the x- and y-terms. To do this, you add the square of half the x-coefficient and the square of half the y-coefficient to both sides of the equation.
For the x's this would be %286%2F2%29%5E2+=+9 and for the y's this would be %28-4%2F2%29%5E2+=+4, so we get:
%28x%5E2%2B6x%2B9%29+%2B+%28y%5E2-4y%2B4%29+=+3%2B9%2B4 Factor the trinomials and simplify.
%28x%2B3%29%5E2+%2B+%28y-2%29%5E2+=+16 Now compare this with the standard form for a circle with centre at (h, k) and radius r.
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 and you can see that the centre (h, k) is at (-3, 2) while the radius is sqrt%2816%29 = 4.
Follow this approach on the second problem and see how you do.
If you still have problems, please re-post.