The diagram shows a sketch of the curve with equation x2−xy+2y2=kx^2 - xy + 2y^2 = kx2−xy+2y2=k, where k k\,k is a positive constant

Show that dydx=2x−yx−4y\displaystyle \frac{dy}{dx} = \frac{2x - y}{x - 4y}dxdy=x−4y2x−y
One of the points on the curve where dydx=0\displaystyle \frac{dy}{dx} = 0dxdy=0 is (277,477)\displaystyle (\frac{2\sqrt{7}}{7}, \frac{4\sqrt{7}}{7})(727,747). Find the value of k k\,k and the coordinates of the other point where dydx=0\displaystyle \frac{dy}{dx} = 0dxdy=0
717 exam-style questions on Edexcel A Level Maths Differentiation, covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change. Each one has a worked solution and a mark scheme showing where the marks go.