A family of circles passing through the points `(3, 7) and (6, 5)` cut the circle `x^2 + y^2 - 4x-6y-3=0`. Show that the lines joining the intersection points pass through a fixed point and find the coordinates of the point.

Consider a family of circles passing through two fixed points A(3,7)&B(6,5) then the chords in which the circle x^(2)+y^(2)-4x-6y-3=0 cuts the members of the family are concurrent at a point.Find the coordinates of this point.

Show that the straight lines x(a+2b)+y(a+3b)=a+b of a and b pass through a fixed point.Find the coordinates of the fixed point.

consider a family of circles passing through two fixed points S(3,7) and B(6,5) . If the common chords of the circle x^(2)+y^(2)-4x-6y-3=0 and the members of the family of circles pass through a fixed point (a,b), then

Centre of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2 is

If circle C passing through the point (2, 2) touches the circle x^2 + y^2 + 4x - 6y = 0 externally at the point (1, 1), then the radius of C is:

Find the equations of the circles passing through the point (-4,3) and touching the lines x+y=2 and x-y=2

The equation of the cirele which passes through the point (1,1) and touches the circle x^(2)+y^(2)+4x-6y-3=0 at the point (2,3) on it is

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.