A curve has the parametric equations
x=sec2t,y=2tant,0<t<π2 x = \sec^2 t, \quad y = 2\tan t, \quad 0 < t < \frac{\pi}{2} x=sec2t,y=2tant,0<t<2πFind an expression for dydx\displaystyle \frac{dy}{dx}dxdy in terms of ttt.
Find an equation of the tangent to the curve when t=π3\displaystyle t = \frac{\pi}{3}t=3π.
Find a cartesian equation for the curve.
Practise Edexcel A Level Maths Parametric Equations with exam-style questions for A Level Maths. 64 questions covering 8.1 Parametric Equations, 8.2 Using Trigonometric Identities, 8.3 Curve Sketching, 8.4 Points of Intersection, and 8.5 Modelling with Parametric Equations, 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.