Prove that the sum of the squares of the reciprocals of two perpendicular diameter of an ellipse is constant.

Variable chords of the parabola passing through a fixed point on the axis,such that sum of the squares of the reciprocals of the two parts of the chords through K ,is a constant.The coordinate of the point K are

A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant then the line passes through-

If two points are taken on the minor axis of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at the same distance from the center as the foci,then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^(2).

A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant.Prove that its locus is an ellipse.

A point moves so that the sum of the squares of the perpendiculars let fall from it on the sides of an equilateral triangle is constant. Prove that its locus is a circle.

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle ABC on the variable line L is equal to 1 then sum of the squares of the reciprocals of the intercepts made by L on the coordinate axes is equal to

If the sum of the roots of ax^(2) + bx + c = 0 is equal to the sum of the squares of their reciprocals, then which one of the following relations is correct?

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.