Let `N` be the foot of perpendicular to the x-axis from point `P` on the parabola `y^2=4a xdot` A straight line is drawn parallel to the axis which bisects `P N` and cuts the curve at `Q ;` if `N O` meets the tangent at the vertex at a point then prove that `A T=2/3P Ndot`

Foot of perpendicular from point P on the parabola y^(2)=4ax to the axis is N. A straight line is drawn parallel to the axis which bisects PN and cuts the curve at Q. If NQ meets the tangent at the vertex A at a point T, then (PN)/(AT) =__________.

A line bisecting the ordinate PN of a point P(at^2,2at),t gt 0 , on the parabola y^2=4ax is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are:

A line bisecting the ordinate PN of a point P(at^(2),2at), t>0,on parabola y^(2)=4ax is drawn parallel to the axis to meet curve at Q.If NO meets meets the tangent at the vertex at Point T.Then the coordinates of T are:

A straight line is drawn parallel to the x-axis to bisect an ordinate PN of the parabola y^(2) = 4ax and to meet the curve at Q. Moreever , NQ meets the tangent at the vertex A of the parabola at T. AT= Knp , then k is equal to

Perpendicular tangents are drawn from an external point P to the parabola y^2=16(x-3) Then the locus of point P is

At a point P on the parabola y^(2) = 4ax , tangent and normal are drawn. Tangent intersects the x-axis at Q and normal intersects the curve at R such that chord PQ subtends an angle of 90^(@) at its vertex. Then

A point P on the parabola y^2=12x . A foot of perpendicular from point P is drawn to the axis of parabola is point N. A line passing through mid-point of PN is drawn parallel to the axis interescts the parabola at point Q. The y intercept of the line NQ is 4. Then-

A normal drawn at a point P on the parabola y^(2)=4ax meets the curve again at O. The least distance of Q from the axis of the parabola,is

Let Q be the foot of the perpendicular from the origin O to the tangent at a point P(alpha, beta) on the parabola y^(2)=4ax and S be the focus of the parabola , then (OQ)^(2) (SP) is equal to

Let P be a point on the parabola, y^(2)=12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line is now drawn through the mid-point M of PN,parallel to its axis which meets the parabola at Q. If the y-intercept of the line NQ is (4)/(3), then