A point is examined with respect to the circle

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

A point P(x1,y1)P(x_1,y_1) is examined with respect to the circle x2+y2+2gx+2fy+c=0x^2 + y^2 + 2gx + 2fy + c = 0. Which one of the following conditions guarantees that PP lies exactly on the circle? (a) (x1+g)2+(y1+f)2=(g2+f2−c)2(x_1+g)^2 + (y_1+f)^2 = (g^2 + f^2 - c)^2 (b) x12+y12+2gx1+2fy1+c>0x_1^2 + y_1^2 + 2g x_1 + 2f y_1 + c > 0 (c) x12+y12+2gx1+2fy1+c=0x_1^2 + y_1^2 + 2g x_1 + 2f y_1 + c = 0 (d) (x1+g)2+(y1+f)2=g2+f2+c(x_1+g)^2 + (y_1+f)^2 = g^2 + f^2 + c

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