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 fixed point. Also find the locus of the middle point of PQ.

Through the vertex A of a parabola the chords AP and AQ are drawn at right angles. Show that the striaght line PQ intersets the axis at a fixed point.

Let P be the point (1,0) and Q a point on the parabola y^(2) =8x, then the locus of mid-point of bar(PQ is-

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is

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 (a) -2tanvarphi (b) -2tan(pi-varphi) (c) 0 (d) 2cotvarphi

A chord overline(PQ) of the parabola y^(2) =4ax , subtends a right angle at the vertex , show that the mid point of overline(PQ) lies on the parabola, y^(2) = 2a (x - 4a) .

If two tangents drawn from a point P to the parabola y^2 = 4x are at right angles, then the locus of P is

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

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

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 .