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 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.

Statement-1: If P(2a,0) be any point on the axis of parabola,then the chord QPR, satisty (1)/((PQ)^(2))+(1)/((PR)^(2))=(1)/(4a^(2)) There exists a point P on the axis of the parabola y^(2)=4ax (other than vertex),such that (1)/((PQ)^(2))+(1)/((PR)^(2))= constant for all QPR of the parabola

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

Find the locus of the middle points of all chords of the parabola y^(2) = 4ax , which are drawn through the vertex.

Perpendicular tangents are drawn from an external point P to the parabola y^2=16(x-3) Then the locus of point P 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-

A curve C has the property that if the tangent drawn at any point P on C meets the co- ordinate axis at A and B, then P is the mid- point of AB. The curve passen through the point (1,1). Determine the equation of the curve.