Chapter 4.2, Problem 61E

To determine

To calculate: The given is equal to $\frac{dy}{dx}$ .

Answer to Problem 61E

The correct option is A.

Explanation of Solution

Given Information: The curve is $x^2-xy+y^2=1$ .

Calculation:

The slope of the curve $x^2-xy+y^2=1$ is,

  $\begin{array}{c}{x}^2-xy+y^2=1\\ 2x-y-x\frac{dy}{dx}+2y\frac{dy}{dx}=0\\ \left(2x-y\right)-\left(x-2y\right)\frac{dy}{dx}=0\\ \left(2x-y\right)=\left(x-2y\right)\frac{dy}{dx}\\ \frac{dy}{dx}=\frac{2x-y}{x-2y}\\ =\frac{-\left(y-2x\right)}{-\left(2y-x\right)}\\ =\frac{\left(y-2x\right)}{\left(2y-x\right)}\end{array}$

Conclusion:

The correct option is A.