Find the angle between the curves  at the points of intersection other than the origin.

To find the angle between the curves \( y^2 = ax \) and \( ay^2 = x^3 \) at their points of intersection other than the origin, we need to follow these steps:

1. **Find the points of intersection:**

   The points of intersection are found by solving the equations simultaneously:
   \[
   y^2 = ax \quad \text{and} \quad ay^2 = x^3.
   \]
   Substitute \( y^2 = ax \) into \( ay^2 = x^3 \):
   \[
   a(ax) = x^3 \implies a^2 x = x^3 \implies x^3 - a^2 x = 0 \implies x(x^2 - a^2) = 0.
   \]
   Thus, the solutions are:
   \[
   x = 0 \quad \text{or} \quad x^2 = a^2 \implies x = \pm a.
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