Let LL' be the latus rectum of the parabola `y^(2)=4ax`and P P' be a double ordinate between the vertex and the latus rectum. Prove that the area of the trapezium L L' P P' is maximum, when the distance of P'P from vertex is `(a)/(9)`.

L L ' is the latus rectum of the parabola y^2 = 4ax and PP' is a double ordinate drawn between the vertex and the latus rectum. Show that the area of the trapezium P P^(prime)L L ' is maximum when the distance P P ' from the vertex is a//9.

If the area bounded by the parabola y^(2) =4ax and its double ordinate x=h is two times the area bounded by its latus rectum prove that h: a , =2^((3)/(2)) : 1.

The parabola y^2=4ax passes through the point (2,-6). Find the length of the latus rectum.

Find the area included between the parabolas y^(2) =16x and the line joining its vertes and an end of latus-rectum

Find the area of the parabola y^(2) = 4ax bounded by its latus rectum.

Length of the focal chord of the parabola y^2=4ax at a distance p from the vertex is:

Let S is the focus of the parabola y^2 = 4ax and X the foot of the directrix, PP' is a double ordinate of the curve and PX meets the curve again in Q. Prove that P'Q passes through focus.

A double ordinate of the parabola y^(2) = 4 ax is of length 8a . Prove that the lines joining the vertex to its two ends are at right angles .

Let P and Q be the points on the prabola y^(2) = 4x so that the line segment PQ subtends right at the vertex . If PQ intersects the axis of the parabola at R , then the distance of the vertex from R is _

Prove that the lines joining the ends of latus rectum of the parabola y^(2) = 4ax with the point of intersection of its axis and directrix are at right angles.