Through the vertex `"O"` of the parabola `y^2=4a x ,` variable chords `O Pa n dO Q` are drawn at right angles. If the variables chord `P Q` intersects the axis of `x` at `R ,` then distance `O R`

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

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.

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=4a x , two chords O Pa n dO Q are drawn and the circles on OP and OQ as diameters intersect at Rdot If theta_1,theta_2 , and varphi are the angles made with the axis by the tangents at P and Q on the parabola and by O R , then value of cottheta_1+cottheta_2 is -2tanvarphi (b) -2tan(pi-varphi) 0 (d) 2cotvarphi

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 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

A chord of parabola y^(2)=4ax subtends a right angle at the vertex The tangents at the extremities of chord intersect on

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) .