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Question

Which of the following equations represents a circle with centre (g,f) and radius g2 + f2 + c ?


A

x2 + y2 + 2gx + 2fy + c = 0

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B

x2 + y2 2gx 2fy + c = 0

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C

x2 + y2 + 2gx + 2fy c = 0

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D

x2 + y2 2gx 2fy c = 0

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Solution

The correct option is D

x2 + y2 2gx 2fy c = 0


Equation of a circle with centre (h,k) and radius r is given by
(xh)2 + (yk)2 = r2

Given, the centre is (g,f) and radius is g2 + f2 + c

(xg)2 + (yf)2 = (g2 + f2 + c)2

x2 + y2 2gx 2fy + g2 + f2 = g2 + f2 + c

x2 + y2 2gx 2fy c = 0


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