If the lengths of the tangents drawn from the point (1,2) to the circles x^2+y^2+x+y-4=0 and 3 x^2+3 y^2-x-y- =0 are in the ratio 3: 4 , then is equal to

Step-by-step solution

aligned & C₁: x^2+y^2+x+y-4=0 & C₂: 3 x^2+3 y^2-x-y- =0 & x^2+y^2- x 3 - y 3 - 3 =0 aligned Length of tangent drawn by an external point is S₁ . Length of tangent drawn from (1,2) to C₁ and C₂ are L₁ and L₂ respectively. aligned L₁ & = S₁ = 1^2+2^2+1+2-4 & = 1+4+1+2-4 = 4 L₁ & =2 aligned L₂= S₁^ = 1^2+2^2- 1 3 - 2 3 - 3 = 4- 3 Given that, L₁ L₂ = 3 4 aligned &= 2 4- 3 = 3 4 [3] 4- 3 =8 & 9 (4- 3 )=64 4- 3 = 64 9 & 4- 64 9 = 3 36-64 9 = 3 & =- 28 3 aligned