Question

X^2 - y^2 = cx

Answer 1

Differentiate both sides with respect to $x$

$$2x-2y\dfrac{dy}{dx}=c$$

Then

$$2x^2-2xy\dfrac{dy}{dx}=cx$$

Substitute

$$2x^2-2xy\dfrac{dy}{dx}=x^2-y^2$$

$$x^2+y^2-2xy\dfrac{dy}{dx}=0$$