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Question

The centre and radius of the circle x2 + y2 + 2gx + 2yf + c=0 are and respectively.


A
g2+f2c
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B
g2+f2+c
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C
(g,f)
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D
(g,f)
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Solution

The correct options are
A g2+f2c
C (g,f)

The general equation of a circle is given x2 + y2 + 2gx + 2yf + c=0 . The centre and radius of this circle are (g,f) and g2 + f2 c respectively ; We will try to get this result.

We know the equation of a circle whose centre is (h,k) and radius r, is (xh)2 + (yk)2 = r2

We will simplify this and compare it with x2 + y2 + 2gx + 2yf + c=0 to find radius and centre.

x2 + y2 2hx 2ky + h2 + k2 r2 = 0 - - - - - (1)

x2 + y2 + 2gx + 2yf + c=0 - - - - - (2)

(1) and (2) represents the same circle.

-h = g and -k = f

(h,k) (g,f)is the centre.

We also have c = h2 + k2 r2 = 0

(h,k)=(g,f)

c = (g)2 + (f)2 r2

r = g2 + f2 c


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