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For the ellipse x²/a² + y²/b² = 1, what is the maximum area of a rectangle that can be drawn inside it?
- ab
- 2ab
- ab/2
- √ab
Correct answer: 2ab
Solution
A rectangle inscribed in x^2/a^2+y^2/b^2=1 with corner (a cosT, b sinT) has area 4*a cosT*b sinT = 2ab sin2T, maximized when 2T=90 deg giving maximum area 2ab.
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