A curve $C$ has equation $x^{2} - xy + y^{2} = 12$. Show that \(\frac{\mathrm{d}y}{\mathrm{

Question

A curve $C$ has equation $x^{2} - xy + y^{2} = 12$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x} = \frac{y - 2x}{2y - x}$. Find the equation of the tangents to the curve that are parallel to the $y$-axis.

Accepted Answer

(a) $\frac{\mathrm dy}{\mathrm dx}=\frac{y-2x}{2y-x}$ (b) $x=4$ and $x=-4$

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

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