Find the locus of the middle points of the chords of the parabola `y^2=4a x` which subtend a right angle at the vertex of the parabola.

Explanation

To find the locus of the midpoints of the chords of the parabola \(y^2 = 4ax\) that subtend a right angle at the vertex, we can follow these steps:

### Step 1: Define the Points on the Parabola
Let the points \(A\) and \(B\) on the parabola be represented by their parametric coordinates:
- \(A(t_1) = (at_1^2, 2at_1)\)
- \(B(t_2) = (at_2^2, 2at_2)\)

### Step 2: Find the Midpoint \(M\) of the Chord \(AB\)
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