Let S be a circle concentric with the circle 3 x^2+3 y^2+x+y-1=0 . If the length of the tangent drawn from a point (2,-2) to the given circle is the radius of the circle S, then the power of the point (2,1) with respect to the circle S is

Step-by-step solution

Given circle is 3 x^2+3 y^2+x+y-1=0 aligned & x^2+y^2+ 1 3 x+ 1 3 y- 1 3 =0 & Centre = (- 1 6 ,- 1 6 ), radius = 14 6 aligned Length of tangents P A , aligned & r₁= O P^2-O A^2 & = (2+ 1 6 )^2+ (-2+ 1 6 )^2- 14 36 = 23 3 aligned Equation of required circle S is (x+ 1 6 )^2+ (y+ 1 6 )^2= 23 3 The power of the point (2,1)=S₁ = (2+ 1 6 )^2+ (1+ 1 6 )^2- 23 3 =- 29 18