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.

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

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

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

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. show that the locus of the centroid of the triangle ABC is x^-2+y^-2+z^-2=p^-2 .

The locus of a point which moves so that the difference of the squares of its distance from two given points is constant, is a

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.

A variable plane passes through a fixed point a,b,c and meet the co-ordinates axes in A,B,C. Show that the locus of the point common to the planes through A,B,C parallel to the co-ordinate planes is a/x+b/y+c/z=1

To find the equation of the hyperbola from the definition that hyperbola is the locus of a point which moves such that the difference of its distances from two fixed points is constant with the fixed point as foci

A variable line makes intercepts on the coordinate axes the sum of whose squares is constant and is equal to a^2 . Find the locus of the foot of the perpendicular from the origin to this line.

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