Question 10
Figure 1 below shows the curve with equation
x2−2xy+4y2−12=0x^2 - 2xy + 4y^2 - 12 = 0x2−2xy+4y2−12=0
a.[3]
Show that
dydx=x−yx−4y\displaystyle \frac{dy}{dx} = \frac{x - y}{x - 4y}dxdy=x−4yx−y
At the point P P\,P on the curve the tangent is parallel to the yyy-axis, and at the point Q Q\,Q on the curve the tangent is parallel to the xxx-axis. The positions of P P\,P and Q Q\,Q are shown in Figure 1.
b.[5]
Show that the exact distance PQ PQ\,PQ is k5k\sqrt{5}k5, where k k\,k is a rational number to be determined.
1.10 G: Differentiation Questions
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.