On the parabola `y^2 = 4ax`, three points `E, F, G` are taken so that their ordinates are in geometrical progression. Prove that the tangents at `E and G` intersect on the ordinate passing through `F`.

If P, Q, R are three points on a parabola y^2=4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on :

If P, Q, R are three points on a parabola y^2=4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on :

If the parabola y^(2) = 4ax passes through the point (3,2) , then the length of its latus rectum is

The tangent and normal at P(t) , for all real positive t , to the parabola y^2= 4ax meet the axis of the parabola in T and G respectively, then the angle at which the tangent at P to the parabola is inclined to the tangent at P to the circle passing through the points P, T and G is

If the normals from any point to the parabola y^2=4x cut the line x=2 at points whose ordinates are in AP, then prove that the slopes of tangents at the co-normal points are in GP.

If the parabola of y^2=4ax passes through the point (3,2), find the length of its latus rectum.

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

Prove that the tangents drawn on the parabola y^(2)=4ax at points x = a intersect at right angle.

If the parabola y^(2) = 4ax passes through the point (4, 1), then the distance of its focus the vertex of the parabola is

The equation of the straight line passing through the point (4. 3) and making intercepts on the co ordinate axes whose sum is -1 , is