A straight line moves in such a maaner that the sum of the reciprocals of its intercepts upon the coordinate axes is always `(1)/(2)` . Show that line always passes through the point (2,2)

A straight line moves in such a manner that the sum of the reciprocals of its intercepts upon the axes is always constant. Show that the line passes throught a fixed point .

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on three coordinate axes is constant . Prove that the plane 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. Prove that the plane passes through a fixed point.

A straight line moves in such a way that the algebraic sum of the perpendicular distance on it form the vertices of a given triangle is always zero. Show that the stright line always passes through the centroid of the triangle.

A straigh line passes through the point (2,3) and is such that the sum of its intercepts on the coordinate axes is 10. Find the equation of the straight line.

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

(b) Determine the value of a if the straight line 2x+ay=10(a-30) passes through the point (1,2)) .

Sum of the reciprocal intercepts on the axes by a moving straight line in its all position remain constant .Show that straight line always passes throguh a fixed point .

Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 always passes through the point (2,3).

Find the locus of the foot of the perpendicular from the origin upon a stright line which always passes through the point (2,3).