PQ is a double ordinate of a parabola `y^2=4a xdot` Find the locus of its points of trisection.

Explanation

To find the locus of the points of trisection of a double ordinate PQ of the parabola \( y^2 = 4ax \), we will follow these steps:

### Step 1: Understand the Double Ordinate
A double ordinate is a line segment that is perpendicular to the axis of the parabola and intersects it at two points. For the parabola \( y^2 = 4ax \), the points of intersection can be represented as \( P(at_1^2, 2at_1) \) and \( Q(at_2^2, 2at_2) \), where \( t_1 \) and \( t_2 \) are parameters corresponding to points P and Q on the parabola.

### Step 2: Define the Points of Trisection
Let the points of trisection be \( C \) and \( D \). The point \( C \) divides the segment \( PQ \) in the ratio \( 1:2 \) and point \( D \) divides it in the ratio \( 2:1 \).

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