Prove that the two circles, which pass through the two points (0, a) and (0, - a) and touch the straight line y =mx + c, will cut ortho- gonally if `c^(2) = a^(2) (2 + m^(2))`.

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) .

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

Equation of straight line passing through the points (2,0) and (0, -3) is

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

Find the equation of the circle which passes through the points (2,3)(4,2) and the centre lies on the straight line y-4x+3=0

The two circles which pass through (0,a) and (0,-a) and touch the line y=mx+c will intersect each other at right angle if a^(2)=c^(2)(2m+1)a^(2)=c^(2)(2+m^(2))c^(2)=a^(2)(2+m^(2))(d)c^(2)=a^(2)(2m+1)

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-