The point P on the parabola `y^(2)=4ax` for which | PR-PQ | is maximum, where R(-a, 0) and Q (0, a) are two points,

Let P(at^(2),2at),Q,R(ar^(2),2ar) be three points on a parabola y^(2)=4ax . If PQ is the focal chord and PK, QR are parallel where the coordinates of k is (2a,0), then the value of r is

If Q is the point on the parabola y ^(2) =4x that is nearest to the point P (2,0) then PQ =

P,Q and R three points on the parabola y^(2)=4ax . If Pq passes through the focus and PR is perpendicular to the axis of the parabola, show that the locus of the mid point of QR is y^(2)=2a(x+a) .

If P(at_(1)^(2), 2at_(1))" and Q(at_(2)^(2), 2at_(2)) are two points on the parabola at y^(2)=4ax , then that area of the triangle formed by the tangents at P and Q and the chord PQ, is

If P(at_(1)^(2), 2at_(1))" and Q(at_(2)^(2), 2at_(2)) are two points on the parabola at y^(2)=4ax , then that area of the triangle formed by the tangents at P and Q and the chord PQ, is

P & Q are the points of contact of the tangents drawn from the point T to the parabola y^(2) = 4ax . If PQ be the normal to the parabola at P, prove that TP is bisected by the directrix.

P & Q are the points of contact of the tangents drawn from the point T to the parabola y^(2) = 4ax . If PQ be the normal to the parabola at P, prove that TP is bisected by the directrix.

If the distances of two points P and Q on the parabola y^(2) = 4ax from the focus of a parabola are 4 and 9 respectively then the distance of the point of intersection of tangents at P and Q from the focus is