Final answer:
The area of the region specified by the equations 25x² - c² and y = c² - 25x² is given directly in the problem statement as 512/15, making that the correct answer. The correct option is A) 512/15.
Step-by-step explanation:
To find the area for the specified region defined by the equations 25x² - c² and y = c² - 25x², we need to find the intersection points of the two equations and calculate the area between them.
Setting the two equations equal to each other:
25x² - c² = c² - 25x²
50x² = 2c²
x² = c²/25
x = ±c/5
The question asks about finding the area of a region bounded by the functions 25x² - c² and y = c² - 25x². It is given that the area for the region is 512/15. This information itself answers the question since the given area is part of the problem statement.
The answer choices are presented to confuse the issue, but the problem has already provided the solution which is the area of the region is 512/15, corresponding to option A). So, despite the additional information provided, the correct area is the one given in the problem, which is 512/15.