another precalc question?

Question

can someone pls explain how to do this crazy equation:

"a rectangle, which is on the 1st quadrant, has one corner on the graph of y=25-x^2, another at the origin, a third on the positive y-axis, and the fourth on the positive x-axis.
1) express the distance 'D' from the point 'P,' which is a corner of the rectangle on the graph, to the origin 'O' as a function of 'X.'
2) express the area of the rectangle 'A' as a function of 'X'
3) what is the domain of 'A'
4) graph A = A(x) "

lol

Answer 1

Point P(x, y) = P(x, 25 - x²).

1) Find the distance D from the origin to P.

D = √(x² + y²) = √[x² + (25 - x²)²]
D = √[x² + 625 - 50x² + x^4]
D = √(x^4 - 49x² + 625)
____________

A = area

2) A = xy = x(25 - x²)
______________

3) What is the domain of A?

What values of x are possible for A? Area must be positive.

Domain is

0 < x < 5