If the length of the tangent drawn from `(f, g)` to the circle `x^2+y^2= 6` be twice the length of the tangent drawn from the same point to the circle `x^2 + y^2 + 3 (x + y) = 0` then show that `g^2 +f^2 + 4g + 4f+ 2 = 0 .`

If the length of the tangent from (f,g) to the circle x^(2)+y^(2)=6 is twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0 , then

If the length of the tangent drawn from (alpha,beta) to the circle x^(2)+y^(2)=6 be twice the length of the tangent from the same point to the circle x^(2)+y^(2)+3x+3y=0, then prove that alpha^(2)+beta^(2)+4 alpha+4 beta+2=0

Find the length of a tangent drawn from the point (3,4) to the circle x ^(2) + y ^(2) - 4x + 6y -3=0.

The length of the tangent drawn from the point (2, 3) to the circles 2(x^(2) + y^(2)) – 7x + 9y – 11 = 0 .

The length of the tangent drawn from the point (2,3) to the circle 2(x^(2)+y^(2))-7x+9y-11=0

The length of the tangent from (0, 0) to the circle 2(x^(2)+y^(2))+x-y+5=0 , is