A Quadrifolium

★ 7/10calculus Parametrization analytic geometry Casework Symmetry

Problem

Consider the curve $C$ with equation

\left(x^2 + y^2\right)^3 = 16x^2y^2.

Determine, with proof, which of the following are true:

1. $C$ is both axially symmetric and centrally symmetric; 2. the only lattice point on $C$ is the origin $(0, 0)$ ; 3. every point of $C$ is within distance $2$ of the origin; 4. the area of the region enclosed by $C$ is greater than $4\pi$ .

Answer

Solution

Difficulty	7/10
Topics	calculus, Parametrization, analytic geometry, Casework, Symmetry

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