A circle touching the line `x +y - 2 = 0` at (1,1) and cuts the circle `x^(2) +y^(2) +4x +5y - 6 = 0` at P and Q. Then

A variable circle which always touches the line x+y-2=0 at (1,1) cuts the circle x^(2)+y^(2)+4x+5y-6=0. Prove that all the common chords of intersection pass through a fixed point.Find that points.

Find k , if the line y = 2x + k touches the circle x^(2) + y^(2) - 4x - 2y =0

The normal at (1,1) to the circle x^(2)+y^(2)-4x+6y-4=0 is

The radius of the circle which touches the line x+y=0 at M(-1,1) and cuts the circle x^(2)+y^(2)+6x-4y+18=0 orthogonally,is

The equation of a circle which touches the line x+y=5 at N(-2,7) and cuts the circle x^(2)+y^(2)+4x-6y+9=0 orthogonally,is

If line 4x + 3y + k = 0 " touches circle " 2x^(2) + 2y^(2) = 5x , then k =