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

The locus of the middle points of the chords of the parabola y^(2)=4ax which pass through the focus, is

Find the locus of the mid-points of the chords of the parabola y^2=4ax which subtend a right angle at vertex of the parabola.

The locus of the point through which pass three normals to the parabola y^2=4ax , such that two of them make angles alpha&beta respectively with the axis & tanalpha *tanbeta = 2 is (a > 0)

What is the value of t such that P(t) and Q(3) are the end points of a focal chord of a parabola y^2 = 4ax ?

Show that the locus of a point that divides a chord of slope 2 of the parabola y^2=4x internally in the ratio 1:2 is parabola. Find the vertex of this parabola.

The ordinates of points P and Q on the parabola y^2=12x are in the ration 1:2 . Find the locus of the point of intersection of the normals to the parabola at P and Q.

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 extremities of focal chord of a parabola are (at_1^2,2at_1) and (at_2^2,2at_2) , then t_1t_2=-1 .

Prove that the chord y-xsqrt2+4asqrt2=0 is a normal chord of the parabola y^2=4ax . Also, find the point on the parabola when the given chord is normal to the parabola.

If a!=0 and the line 2bx+3cy+4d=0 passes through the points of intersection of the parabola y^2 = 4ax and x^2 = 4ay , then