Two circles which pass through the points `A(0, a), B (0,-a)` and touch the line `y = mx+c` wil cut orthogonally if

Prove that the two circles each of which passes through the point (0, k) and (0, -k) and touches the line y=mx+b will cut orthogonally, if b^2 = k^2 (2+m^2) .

P(a,b) is a point in first quadrant.If two circles which passes through point P and touches both the coordinate axis,intersect each other orthogonally,then

The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle x^(2)+y^(2)=9 , is

The locus of the centere of a circle which passes through the point (0,0) and cuts off a length 2b from the line x=c is-

Find the equation of the circle passing through the point (1,9), and touching the line 3x + 4y + 6 = 0 at the point (-2,0) .

A circle passes through the points (0,0) and (0,1 ) and also touches the circie x^(2)+y^(2)=16 The radius of the circle is

The radius of the least circle passing through the point (8,4) and cutting the circle x^(2)+y^(2)=40 orthogonally is