If a circle passes through the point `(a, b)` and cuts the circle `x^2 +y^2=k^2` orthogonally, then the equation of the locus of its center is

If a circle Passes through a point (1,2) and cut the circle x^2+y^2 = 4 orthogonally,Then the locus of its centre is

A circle passes through the origin and has its center on y=x If it cuts x^2+y^2-4x-6y+10=- orthogonally, then find the equation of the circle.

A circle passes through (0,0) and (1, 0) and touches the circle x^2 + y^2 = 9 then the centre of circle is -

If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0 at A and B , then the maximum of PA+PB is

If a circle passes through the point (0,0),(a ,0)a n d(0, b) , then find its center.

A variable circle passes through the point A(a ,b) and touches the x-axis. Show that the locus of the other end of the diameter through A is (x-a)^2=4b y .

The normal at the point (3, 4) on a circle cuts the circle at the point (-1,-2). Then the equation of the circle is

Find the circle of minimum radius which passes through the point (4, 3) and touches the circle x^2+y^2=4 externally.

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

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is