A variable circle has the equation

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

Problem

A variable circle CC has the equation x2+y2−2(t2−3t+1)x−2(t2+2t)y+t=0x^2 + y^2 - 2(t^2 - 3t + 1)x - 2(t^2 + 2t)y + t = 0 , where tt is a parameter. If the power of point (a,b)(a,b) w.r.t. the circle CC is constant, then the ordered pair (a,b)(a,b) is (1) (110,−110)\left(\frac{1}{10}, -\frac{1}{10}\right) (2) (110,110)\left(\frac{1}{10}, \frac{1}{10}\right) (3) (−110,110)\left(-\frac{1}{10}, \frac{1}{10}\right) (4) (−110,−110)\left(-\frac{1}{10}, -\frac{1}{10}\right)

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