If normal to the parabola `y^2-4a x=0` at `alpha` point intersects the parabola again such that the sum of ordinates of these two points is 3, then show that the semi-latus rectum is equal to `-1. 5alphadot`

If normal to parabola y^(2)=4ax at point P(at^(2),2at) intersects the parabola again at Q, such that sum of ordinates of the points P and Q is 3, then find the length of latus ectum in terms of t.

If the normal to the parabola y^2=4a x at point t_1 cuts the parabola again at point t_2 , then prove that t_2 2geq8.

A circle and a parabola y^2=4a x intersect at four points. Show that the algebraic sum of the ordinates of the four points is zero. Also show that the line joining one pair of these four points is equally inclined to the axis.

Find the area of the parabola y^2=4ax and its latus rectum.

If the normals to the parabola y^2=4a x at the ends of the latus rectum meet the parabola at Q and Q^(prime), then Q Q^(prime) is

Find the equations of normal to the parabola y^2=4a x at the ends of the latus rectum.

Tangents are drawn to the parabola y^2=4a x at the point where the line l x+m y+n=0 meets this parabola. Find the point of intersection of these tangents.

Find the coordinates of the focus , axis, the equation of the directrix and latus rectum of the parabola y^(2)=8x .

If two normals to a parabola y^2 = 4ax intersect at right angles then the chord joining their feet pass through a fixed point whose co-ordinates are:

If normal at point P on the parabola y^2=4a x ,(a >0), meets it again at Q in such a way that O Q is of minimum length, where O is the vertex of parabola, then O P Q is