Doubt from parabola

4th

Intuitively, it seems like the angle is 90°.

Why? For all other cases, your sides would increase by a lot.

If you want to solve it rigorously, you have to consider an arbitrary point on the parabola( take parametric), write the normal equation and find it's intersection on the parabola again.

Write the tangent equations for both, find their intersection, and compute the area.

The angle in the answer is 45

If it is 45°, then 135° should be valid too!

Try solving rigorously once, and see if it checks out.