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 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. Thinking Process : For line which makes intercepts on axis (x)/(a) + (y)/( b) = 1 If (1)/( a) + (1)/( b) = constant ( (1)/(k) ) then ( k)/( a) + (k)/( b) =1 and we say if passes from point (k,k) .

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

Show that the curve for which the normal at every point passes through a fixed point is a circle.

Find equation of the circle passing through (0,0) and making intercepts a and b on the coordinate axes.

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.

Equation of line passing through a point (1, 4) and the sum of the intercept on the positive axes is minimum is …………..

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that the locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.