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) (0,(4/3)at) (b) (0,2at) (c) ((1/4)at^2,at) (d) (0,at)

Find the locus of point on the curve y^2=4a(x+asin (x/a)) where tangents are parallel to the axis of xdot

The length of the foot of perpendicular drawn from the point P(3, 6, 7) on y-axis is

L is the foot of perpendicular drawn from a point P(3,4,5) on x-axis. The coordinates of L are

The coordinates of the foot of perpendicular drawn from the point P(-2,5,4) on the x-axis are

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 Q. The least distance of Q from the axis of the parabola, is

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

Prove that points of the curve y^2=4a{x+asin(x/a)} at which tangents are parallel to x-axis lie on the parabola.