A normal drawn to the parabola `y^2=4a x` meets the curve again at `Q` such that the angle subtended by `P Q` at the vertex is `90^0dot` Then the coordinates of `P` can be (a)`(8a ,4sqrt(2)a)` (b) `(8a ,4a)` (c)`(2a ,-2sqrt(2)a)` (d) `(2a ,2sqrt(2)a)`

If normal at point P on the parabola y^2=4a x ,(a >0), meets it again at Q in such a way that O Q is of minimum length, where O is the vertex of parabola, then O P Q is

If the tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Q and Q^(prime), then Q Q^(prime) is

A is a point on the parabola y^2=4a x . The normal at A cuts the parabola again at point Bdot If A B subtends a right angle at the vertex of the parabola, find the slope of A Bdot

If the normals to the parabola y^2=4a x at P meets the curve again at Q and if P Q and the normal at Q make angle alpha and beta , respectively, with the x-axis, then t a nalpha(tanalpha+tanbeta) has the value equal to 0 (b) -2 (c) -1/2 (d) -1

A square has one vertex at the vertex of the parabola y^2=4a x and the diagonal through the vertex lies along the axis of the parabola. If the ends of the other diagonal lie on the parabola, the coordinates of the vertices of the square are (a) (4a ,4a) (b) (4a ,-4a) (c) (0,0) (d) (8a ,0)

Tangents are drawn from any point on the line x+4a=0 to the parabola y^2=4a xdot Then find the angle subtended by the chord of contact at the vertex.

An equilateral triangle S A B is inscribed in the parabola y^2=4a x having its focus at Sdot If chord A B lies towards the left of S , then the side length of this triangle is (a) 2a(2-sqrt(3)) (b) 4a(2-sqrt(3)) (c) a(2-sqrt(3)) (d) 8a(2-sqrt(3))

The tangents to the parabola y^2=4a x at the vertex V and any point P meet at Q . If S is the focus, then prove that S P,S Q , and S V are in GP.

Normals are drawn at point P,Q,R lying on parabola y 2 =4x which intersect at (3,0) then area of △PQR is :-