Application of DerivativeHard
Question
The dimensions of the rectangle of maximum area that can be inscribed in the ellipse
(x/4)2 + (y/3)2 = 1 are
(x/4)2 + (y/3)2 = 1 are
Options
A.√8, √2
B.4, 3
C.2, √8, 3√2
D.√2, √6
Solution
x = 4 cosθ, y = 3 sin θ
Let A be area.
A = 4 (4 cos θ) (3 sin θ)
= 24 sin 2θ
A is maximum when 2 θ = π/2
⇒ Dimensions are
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