A Mutated Ellipse

★ 8/10calculus Affine Transformation Cauchy-Schwarz analytic geometry inequality

Problem

For $a, b \geqslant 2$ and $n \in \mathbb{N}^*$ , let $S_n$ be the area enclosed by the closed curve

E_n \colon \frac{x^{2^n}}{a^2} + \frac{y^{2^n}}{b^2} = 1.

Prove that $4 < S_n \leqslant ab\pi$ .

Answer

Solution

Difficulty	8/10
Topics	calculus, Affine Transformation, Cauchy-Schwarz, analytic geometry, inequality

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