Find nouns of Rectangle inside of Ellipse - Calc.?

How do you find the largest possible area of a rectiangle inside of an ellipse simply near the knowledge that

(x2/144) + (y2/16) = 1

(That is surrounded by words x squared plus y squared equals 1)

Answers:    Using the parametric equations of the ellipse:
x = 12 cos(t)
y = 4 sin(t),
the area of a rectangle next to one vertex at the point t is:
= 4 * 12 * 4 sin(t)cos(t)
= 96 sin(2t)
This has its maximum effectiveness when sin(2t) = 1, and the area is after 96.

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