Prove that the length of a focal chord of a parabola varies inversly as the square of its distance from the vertex.

Prove that the length of a focal chord of a parabola varies inversely as the square of its distance from the vertex.

Show that the temperature of a planet varies inversely as the square root of its distance from the sum.

Prove that the perpendicular focal chords of a rectangular hyperbola are equal.

If the length of a focal chord of the parabola y^2=4a x at a distance b from the vertex is c , then prove that b^2c=4a^3 .

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

Prove that the tangent at one extremity of the focal chord of a parabola is parallel to the normal at the other extremity.

A point moves such that the sum of the squares of its distances from the two sides of length ‘a’ of a rectangle is twice the sum of the squares of its distances from the other two sides of length b. The locus of the point can be:

Prove that the circle described on the focal chord of parabola as a diameter touches the directrix

Circles are described on any focal chords of a parabola as diameters touches its directrix

Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is (a) 8 (b) 6sqrt(2) (c) 9 (d) 5sqrt(3)