A curve has the parametric equations
x=ln(t+1),y=t2−5,t>−1 x = \ln(t + 1), \quad y = t^2 - 5, \quad t > -1 x=ln(t+1),y=t2−5,t>−1Verify that the points where the curve crosses the coordinate axes are (ln(5+1),0)(\ln(\sqrt{5}+1),0)(ln(5+1),0) and (0,−5)(0,-5)(0,−5).
Verify that an equation for the tangent to the curve when t=3t = 3t=3 is
y=24x+4−24ln4 y = 24x + 4 - 24\ln 4 y=24x+4−24ln4215 exam-style questions on Edexcel A Level Maths Parametric Equations, 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. Each one has a worked solution and a mark scheme showing where the marks go.