Question

What is the radius of curvature of the curve xy = c^2 at (c,c)?

(a) c

(b) 2

(c) 2c

(d) √2 c

The question was asked in a job interview.

This intriguing question comes from Evolutes topic in division Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (d) √2 c

Best explanation: y = c^2/x

Integrating,

\(y_1 = \frac{-c^2}{x^2} = \frac{-c^2}{c^2} = -1\)

\(y_2 = \frac{2c^2}{x^3} =  \frac{2c^2}{c^3} = \frac{2}{c}\)

Radius of curvature = \(\frac{\left(1+y_{1}^{2}\right)^\frac{3}{2}}{y_2} = \frac{\left(1+1\right)^\frac{3}{2}}{\frac{2}{c}} = \frac{c.2^{\frac{3}{2}}}{2} = \sqrt{2}c.\)