A straight line cuts intercepts from the axes of coordinates the sum of whose reciprocals is a constant. Show that it always passes though as fixed point.

A straight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

Astraight line moves so that the sum of the reciprocals of its intercepts made on axes is constant. Show that the line passes through a fixed point.

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the three coordinate axes is constant. Show that the plane 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

A variable line makes intercepts on the coordinate axes the sum of whose squares is constant and is equal to a . Find the locus of the foot of the perpendicular from the origin to this line.

The line which cuts off equal-intercept from the axes and pass through the point (1,-2) is.

The locus of the centre of circle which cuts off an intercept of constant length on the x-axis and which passes through a fixed point on the y-axis, is

The straight line whose sum of the intercepts on theaxes is equal to half of the product of the intercepts,passes through the point whose coordinates are

If a variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is 1/2 , then the plane passes through the point

Two straight lines pass through the fixed points (+-a, 0) and have slopes whose products is pgt0 Show that the locus of the points of intersection of the lines is a hyperbola.