Worked Example 2
A curve $C$ has equation ${{x}^{2}}-xy+{{y}^{2}}=12$.
(a)
Show that $\frac{\text{d}y}{\text{d}x}=\frac{y-2x}{2y-x}$.
(b)
Find the equation of the tangents to the curve that are parallel to $y-$axis.
A curve $C$ has equation ${{x}^{2}}-xy+{{y}^{2}}=12$.
(a)
Show that $\frac{\text{d}y}{\text{d}x}=\frac{y-2x}{2y-x}$.
(b)
Find the equation of the tangents to the curve that are parallel to $y-$axis.