The locus of the points of trisection of the double ordinates of a parabola is a

Let us assume that the parabola be y² = 4ax.

The parametric equations of the points on the parabola are (at², 2at).

If we assume the points of extremities of the double ordinate of the parabola (at², 2at) and (at², - 2at).

We know that the point of trisection is the point in between these point at a ratio of 2:1 or 1:2.

Let us take the ratio to be 1:2.

Let us assume the point of trisection be (x, y).

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Consider y²,

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The locus of point of trisection is parabola.

∴The correct option is C