A micro-robotic probe moves along a path C C\,C within a high-precision magnetic field. The relationship between its horizontal displacement x x\,x and its vertical displacement y y\,y is defined by the equation
x=3sec24y,x>3,0<y<π8x = 3\sec^2 4y, \quad x > 3, \quad 0 < y < \frac{\pi}{8}x=3sec24y,x>3,0<y<8π
Find an expression for dxdy\dfrac{dx}{dy}dydx in terms of yyy.
Hence show that dydx=pqxx−3\dfrac{dy}{dx} = \frac{p}{qx\sqrt{x-3}}dxdy=qxx−3p where p p\,p is irrational and q q\,q is an integer, stating the values of p p\,p and qqq.
Find the equation of the normal to the probe's path C C\,C at the point where y=π12\displaystyle y = \frac{\pi}{12}y=12π, giving your answer in the form y=mx+cy = mx + cy=mx+c where m m\,m and c c\,c are exact constants.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.