Home
Class 12
MATHS
Through the vertex O of a parabola y^(2)...

Through the vertex O of a parabola `y^(2) = 4x` chords OP and OQ are drawn at right angles to one another. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point.

Text Solution

Verified by Experts

The correct Answer is:
`2a`
Promotional Banner

Similar Questions

Explore conceptually related problems

Through the vertex 'O' of parabola y^(2)=4x chords OP and OQ are drawn at right angles to one another.Show that for all positions of P, PQ cuts the axis of the parabola at a fixixed point.Also find the locus of the middle point of PQ.

Through the vertex of the parabola y^(2)=4ax , chords OA and OB are drawn at right angles to each other . For all positions of the point A, the chord AB meets the axis of the parabola at a fixed point . Coordinates of the fixed point are :

Through the vertex O of the parabola y^(2)=4ax, variable chords O Pand OQ are drawn at right angles.If the variables chord PQ intersects the axis of x at R, then distance OR

Through the vertex ' O^(prime) of the parabola y^2=4a x , variable chords O Pa n dO Q are drawn at right angles. If the variable chord P Q intersects the axis of x at R , then distance O R : (a)equals double the perpendicular distance of focus from the directrix. (b)equal the semi latus rectum of the parabola (c)equals latus rectum of the parabola (d)equals double the latus rectum of the parabola

The vertex A of the parabola y^(2)=4ax is joined to any point P on it and PQ is drawn at right angles to AP to meet the axis in Q. Projection of PQ on the axis is equal to

If from the vertex of a parabola y^(2)=4x a pair of chords be drawn at right angles to one another andwith these chords as adjacent sides a rectangle be made,then the locus of the further end of the rectangle is

If from the vertex of the parabola y^(2)=4ax , a pair of chords be drawn at right angles to one another and with these chords as adjacent sides, a rectangle be drawn, prove that the locus of the vertex of the rectangle, farthest from origin, is the parabola y^(2)=4a(x-8a) .

Through the vertex O of the parabola y^(2) = 4ax , a perpendicular is drawn to any tangent meeting it at P and the parabola at Q. Then OP, 2a and OQ are in