prove that for a suitable point `P` on the axis of the parabola, chord `A B` through the point `P` can be drawn such that `[(1/(A P^2))+(1/(B P^2))]` is same for all positions of the chord.

prove that for a suitable point P on the axis of the parabola,chord AB through the point P can be drawn such that [((1)/(AP^(2)))+((1)/(BP^(2)))] is same for all positions of the chord.

Prove that on the axis of any parabola there is a certain point 'k' which has the property that, if a chord PQ of parabola be drawn through it then (1)/((PK)^(2))+(1)/((QK)^(2)) is the same for all positions of the chord.

Prove that on the axis of any parabola there is a certain point 'k' which has the property that, if a chord PQ of parabola be drawn through it then 1/(PK)^2+1/(QK)^2 is the same for all positions of the chord.

Prove that on the axis of any parabola there is a certain point 'k' which has the property that, if a chord PQ of parabola be drawn through it then 1/(PK)^2+1/(QK)^2 is the same for all positions of the chord.

Let P be the midpoint of a chord joining the vertex of the parabola y^(2) = 8x to another point on it . Then locus of P .

PRQ is a variable chord of y^(2)=4ax and R is a point on the axis of the parabola such that (1)/(PR^(2))+(1)/(QR^(2)) is independent of slope bar(P)O then the point R is

TP&TQ are tangents to the parabola,y^(2)=4ax at P and Q. If the chord passes through the point (-a,b) then the locus of T is

P(1,1) is a point on the parabola y=x^(2) whose vertex is A. The point on the curve at which the tangent drawn is parallel to the chord bar(AP) is

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-