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 the parabola. 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 OPQ is 3 sqrt(2) , then which of the following is (are) the coordinates of P ?

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 sqrt 2 , then which of the following is (are) the coordinates of P? (a) ( 4 , 2 √ 2 ) (b) ( 9 , 3 √ 2 ) (c) ( 1 4 , 1 √ 2 ) (d) ( 1 , √ 2 )

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

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex 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)

The coordinates of the vertex of the parabola (x + 1)^(2) =- 9(y +2) are

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2) = 2ax

Show that the locus of the middle points of chords of the parabola y^(2) = 4ax passing through the vertex is the parabola y^(2)= 2ax .

A normal chord of the parabola y^2=4ax subtends a right angle at the vertex, find the slope of chord.