The equation of a curve $C$ is $x^2 - 2xy + 2y^2 = k$, where $k$ is a constant. Find \(\f

Question

The equation of a curve $C$ is $x^2 - 2xy + 2y^2 = k$, where $k$ is a constant. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$. Given that $C$ has two points for which the tangents are parallel to the line $y = x$, find the range of values of $k$.

Accepted Answer

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y-x}{2y-x}$, $k>0$

Techniques of Differentiation - Implicit Differentiation

Techniques of Differentiation - Implicit Differentiation

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