Home
Class 12
MATHS
Prove that on the axis of any probabla t...

Prove that on the axis of any probabla 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.

Promotional Banner

Similar Questions

Explore conceptually related problems

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 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 all the chords of a circle through a given point within it, the least is one which is bisected at that point.

Prove that all the chords of a circle through a given point within it, the least is one which is bisected at that point.

Show that all chords of a parabola which subtend a right angle at the vertex pass through a fixed point on the axis of the curve.

From the origin, chords are drawn to the circle (x-1)^2 + y^2 = 1 . The equation of the locus of the mid-points of these chords

Let the focus S of the parabola y^2=8x lies on the focal chord PQ of the same parabola . If PS = 6 , then the square of the slope of the chord PQ is

The normals at the extremities of a chord PQ of the parabola y^2 = 4ax meet on the parabola, then locus of the middle point of PQ is

If the point P(4, -2) is the one end of the focal chord PQ of the parabola y^(2)=x, then the slope of the tangent at Q, is

The locus of the point of intersection of normals at the points drawn at the extremities of focal chord the parabola y^2= 4ax is