How do you find the length of the radius, and the centre of this circle
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How do you find the length of the radius, and the centre of this circle

[From: ] [author: ] [Date: 11-05-30] [Hit: ]
2gx=-3x i.e. g=-3/2f=-5/2. Centre =(-g,-f) C=(3/2,Radius=sqrt g^+f^-cr=3.......
(2x-3)^2 + (2y-5)^2 = 36

For the radius, I'd usually square root the 36, but because of the '2' in front of the x and y, then I can't seem to figure it out. My text book at the back says (according to the graph) the radius is 5/2.

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(2x - 3)^2 + (2y - 5)^2 = 36
[2(x - 3/2)]^2 + [2(y - 5/2)^2 = 36
4(x - 3/2)^2 + 4(y - 5/2)^2 = 36
(x - 3/2)^2 + (y - 5/2)^2 = 9 (dividing both sides by 4)

so the center is (3/2 , 5/2), and the radius is 3
(since the radius squared is 9)

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Expand the given equation you will get
4x^+4y^-12x-20y-2=0. Divide both sides by 4 to obtain the general formula of circle
x^+y^-3x-5y-1/2=0. 2gx=-3x i.e. g=-3/2 f=-5/2. Centre =(-g,-f) C=(3/2,5/2)
Radius=sqrt g^+f^-c
r=3.
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