Prove that the semi-latusrectum of the parabola `y^2=4ax` is the harmonic mean between the segments of any focal chord of the parabola.

Prove that the semi-latus rectum of the parabola y^(2) = 4ax is the harmonic mean between the segments of any focal chord of the parabola.

The focus of the parabola y^2= 4ax is :

The directrix of the parabola y^2=4ax is :

If l denotes the semi-latus rectum of the parabola y^2= 4ax and SP and SQ denote the segments of any focal chord PQ, S being the focus, then SP, l and SQ are in the relation :

Find the focus of the parabola x^2=4y

The vertex of the parabola y^2=4a(x+a) is:

Statement I: The lines from the vertex to the two extremities of a focal chord of the parabola y^2=4ax are perpendicular to each other. Statement II: If the extremities of focal chord of a parabola are (at_1^2,2at_1) and (at_2^2,2at_2) , then t_1t_2=-1 .

The locus of the middle points of normal chords of the parabola y^2 = 4ax is-