A straight line moves so that the sum of the reciprocals of its intercepts an axes is constant, show that it passes through a fixed point.

A variable plane moves so that the sum of reciprocals of its intercepts on the three coordinate axes is constant, show that it passes through a fixed point.

A variable line cuts n given concurrent straight lines at A_1,A_2...A_n such that sum_(i=1)^n 1/(OA_i) is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

The graph of the line x=3 passes through the point:

Find the equation of a line that cuts off equal intercepts on the co-ordinate axes and passes through the point (5, 6).

Find the equation of a line that cuts off equal intercepts on the coordinate axis and passes through the point (2, 3).

Show that the sum of the reciprocals of the intercepts on rectangular axes made by a fixed plane is same for all systems of rectangular axes, with a given origin.

The equation of line which makes equal intercepts on axis and passes through the point (2,3) is: