A curve has the equation x2−xy+y2=12x^2 - xy + y^2 = 12x2−xy+y2=12
The gradient of the tangent to the curve is 1 at the points P P\,P and QQQ.
Show that x+y=0x + y = 0x+y=0 at P P\,P and QQQ.
Find the coordinates of P P\,P and QQQ.
375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.