Area of region bounded by three parabolas?
These three parabolas were correct responses to an earlier question.
x² - 40x - 16y + 144 = 0
9x² + 24xy + 16y² - 360x - 288y + 1296 = 0
9x² - 24xy + 16y² - 360x - 288y + 1296 = 0
The points A(0, 9), B(4, 0), and C(36, 0) lie on all three curves. What is the area of the region on the interior of all three parabolas? Exact answers only, please.