(a) Show that $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u…

Question

(a) Show that $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$, where $u = \tan^{-1}\left(\frac{y}{x}\right)$.

(b) Find the position and nature of double point on $a^2y^2 = a^2x^2 - 4x^3$.

(c) Find the radius of curvature at any point of the cardioid $r = a(1 - \cos\theta)$.

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• Partial Differentiation — topic
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