Let PQ be a chord of the parabola `y^2=4x`. A circle drawn with PQ as a diameter passes through the vertex V of theparabola. If `ar(Delta PVQ)=20` sq unit then the coordinates of P are

Let P and Q be distinct points on the parabola y^2 = 2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle Delta OPQ is 3 √2 , then which of the following is (are) the coordinates of P?

Length of the focal chord of the parabola (y +3)^(2) = -8(x-1) which lies at a distance 2 units from the vertex of the parabola is

Find the locus of the middle points of the chords of the parabola y^2=4a x which subtend a right angle at the vertex of the parabola.

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)

If (a ,b) is the midpoint of a chord passing through the vertex of the parabola y^2=4x, then prove that 2a=b^2

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

PQ is any focal chord of the parabola y^(2)=8 x. Then the length of PQ can never be less than _________ .

A circle is drawn to pass through the extremities of the latus rectum of the parabola y^2=20 x . It is given that this circle also touches the directrix of the parabola, Find the radius of this circle.

The triangle PQR of area 'A' is inscribed in the parabola y^2=4ax such that the vertex P lies at the vertex pf the parabola and base QR is a focal chord.The modulus of the difference of the ordinates of the points Q and R is :

A circle is drawn to pass through the extremities of the latus rectum of the parabola y^2=8xdot It is given that this circle also touches the directrix of the parabola. Find the radius of this circle.