Find the area of the region bounded by x2 + 16y = 0 and its latus rectum.

This is a simple problem of the area under the two curves.

Step 1: Find the latus rectum and its intersection points with the parabola.

As following the above questions procedure:

We find the equation of latus rectum as

And the intersection points:

Step 2: Integrating the expression to find the area enclosed by the curves.