SOLUTION: Question: Find the center and radius of x^2+y^2-6x-2y-6=0 Possible Answers: (A) none of these (B) center (3,1) radius 16 (C) center (3,1) radius 4 (D) center (-3,-1) radius

Question 30361: Question:
Find the center and radius of x^2+y^2-6x-2y-6=0
Possible Answers:
(A) none of these
(B) center (3,1) radius 16
(C) center (3,1) radius 4
(D) center (-3,-1) radius 16
Thanks!
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
x^2+y^2-6x-2y-6=0
A circle, of radius r, and centred on the point (h,k) can be written as,
(x-h)� + (y-k)� = r�
expanding this expression,
x� - 2hx + h� + y� - 2ky + k� = r�
x� + y� - 2hx - 2ky + (h� + k� - r�) = 0
comparing this with the expression we were given,
x^2+y^2-6x-2y-6=0
and comparing coefficients,
-2h = -6
-2k = -2
h� + k� - r� = -6
From the 1st two eqns,
h = 3
=====
k = 1
=====
substituting for h=3 and k=1 into the 3rd eqn,
9 + 1 - r� = -6
-r� = -16
r� = 16
r = 4
=====
We therefore have: (h,k) = (3,1) and r = 4
============================================
Ans:C
=====

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