The locus of the centre of the circle passing through the origin O and the points of intersection A and B of any line through (a, b) and the coordinate axes is

If the centre of the circle passing through the origin and the point of intersecton of the pair of straingth lines xy - 7x + 3y -21=0 with the coordinate axes lies on the x + y =k, then k is equal to.

Equations of the line passing through the origin and the point (a,b,c) are

The locus of centre of a circle which passes through the origin and cuts off a length of 4 units on the line x=3 is

Find the equation of the straight line passing through the origin and the point of intersection of the lines x/a + y/b = 1 and x/b + y/a = 1.

The locus of the centres of circles passing through the origin and intersecting the fixed circle x^(2)+y^(2)-5x+3y-1=0 orthogonally is

The equation of any circle passing through the points of intersection of the circle S=0 and the line L=0 is

Find the equation of a circle which passes through the origin and whose centre is (a, b).

Find the equation of the circle passing through the origin and the points where the line 3x+4y=12 meets the axes of coordinates.