Find the values of c such that the area of the region bounded by the parabolas y = 16x2 − c2 and y = c2 − 16x2 is 250/3. (enter your answers as a comma-separated list.)

First, note that these two parabolas are symmetric about the x-axis. The first one has its branches up in y-direction and the second one has its branches down in y-direction. This means that if you want to find area of the region bounded by the parabolas, you can find area of the region bounded by second parabola and x-axis and multiply it by 2.

1. Find x-intercepts of parabola

When y=0, you have

2. Find area:

Then the area of the region bounded by the parabolas is

3. Since this area is you have

c=5.