Circle with parameter

Geometry Level pending

A variable circle C C has the equation x 2 + y 2 − 2 ( t 2 − 3 t + 1 ) x − 2 ( t 2 + 2 t ) y + t = 0 x^2+y^2-2(t^2-3t+1)x-2(t^2+2t)y+t=0 , where t t is a parameter. If the power of the point P ( a , b ) P(a,b) with respect to the circle C C is constant then find the ordered pair ( a , b ) (a,b) .

( − 1 10 , 1 10 ) \left(-\frac{1}{10},\frac{1}{10}\right) ( 1 10 , − 1 10 ) \left(\frac{1}{10},-\frac{1}{10}\right) ( 1 10 , 1 10 ) \left(\frac{1}{10},\frac{1}{10}\right) ( − 1 10 , − 1 10 ) \left(-\frac{1}{10},-\frac{1}{10}\right)

Sahil Silare by Sahil Silare , 20, India

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