Math Problem Statement
Find the radii of curvature of the curve y ^ 2 * (a - x) = x ^ 2 * (a + x) at the origin.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Implicit Differentiation
Curvature
Formulas
Implicit Differentiation: d/dx[f(y) * g(x)]
Radius of Curvature Formula: R = (1 + (dy/dx)^2)^(3/2) / |d^2y/dx^2|
Theorems
Curvature and Radius of Curvature Theorem
Suitable Grade Level
Undergraduate Calculus