`L L '` is the latus sectum of the parabola `y^2=4a xa n dP P '` 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.`

Let p be a point on the parabola y^(2)=4ax then the abscissa of p ,the ordinates of p and the latus rectum are in

Distance between an end of a latus-rectum of the parabola y^(2) = 16x and its vertex is

If 0 is the vertex and L,L' are the extremities of the latusrectum of the parabola y^(2)=4ax then the area of the triangle OLL' is

In the parabola y^2 = 4x , the ends of the double ordinate through the focus are P and Q. Let O be the vertex. Then the length of the double ordinate PQ is

Distance of a point P on the parabola y^(2)=48x from the focus is l and its distance from the tangent at the vertex is d then l-d is equal to

A double ordinate of the parabola y^(2)=8px is of length 16p. The angle subtended by it at the vertex of the parabola is

For the parabola y^(2)=4px find the extremities of a double ordinate of length 8p. Prove that the lines from the vertex to its extremities are at right angles.

If L and L' are ends of latus rectum of the parabola 9y^(2)=4x then the combined equation of OL and OL' is

If the bisector of angle A P B , where P Aa n dP B are the tangents to the parabola y^2=4a x , is equally, inclined to the coordinate axes, then the point P lies on the tangent at vertex of the parabola directrix of the parabola circle with center at the origin and radius a the line of the latus rectum.