If the length of the tangent from a point (f,g) to the circle `x^2+y^2=4` be four times the length of the tangent from it to the circle `x^(2)+y^(2)=4x`, show that `15f^(2)+15g^(2)-64f+4=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

Show that if the length of the tangent from a point P to the circle x^2 + y^2 = a^2 be four times the length of the tangent from it to the circle (x-a)^2 + y^2 = a^2 , then P lies on the circle 15x^2 + 15y^2 - 32ax + a^2=0 .

The length of tangent from the point (2,-3) to the circle 2x^(2)+2y^(2)=1 is

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

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

The length of tangent from (0,0) to the circle x^(2)+y^(2)-14x+12y+25=0