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 AB be a chord of the parabola x^(2) = 4y . A circle drawn with AB as diameter passes through the vertex C of the parabola. If area of DeltaABC = 20 sq . units then the coordinates of A can be

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 )

The locus of mid - points of all chords of parabola y^(2)=4x, for which all cirlces drawn taking them as diameters passes through the vertex of the parabola is a conic whose length of the smallest focal chord is equal to

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

Write the length of the chord of the parabola y^2=4a x which passes through the vertex and in inclined to the axis at pi/4 .

Let PQ be a focal chord of the parabola y^(2)=4x . If the centre of a circle having PQ as its diameter lies on the line sqrt5y+4=0 , then length of the chord PQ, is

Let PQ be a focal chord of the parabola y^(2)=4ax . If the centre of a circle having PQ as its diameter lies on the line sqrt5y+4=0 , then length of the chord PQ, is

Prove that the locus of the middle points of all chords of the parabola y^2 = 4ax passing through the vertex is the parabola y^2 = 2ax .

A circle of radius 4 drawn on a chord of the parabola y^(2)=8x as diameter touches the axis of the parabola. Then the slope of the chord is

In the parabola y^(2) = 4ax , the length of the chord passing through the vertex and inclined to the x-axis at (pi)/(4) is