The curve C C\,C has parametric equations
x=t2−4x = t^2 - 4x=t2−4, y=t3−4ty = t^3 - 4ty=t3−4t, t∈Rt \in \mathbb{R}t∈R
Show that C C\,C crosses itself at the origin, and state the two values of t t\,t for which C C\,C passes through the origin.
Find an equation of the tangent to C C\,C at the point where t=2t = 2t=2.
Hence write down an equation of the other tangent to C C\,C at the origin.
143 exam-style questions on OCR A Level Maths 1.3 Coordinate Geometry in the x-y Plane, covering 1.3.1 Straight lines, 1.3.2 Parallel and perpendicular lines, 1.3.3 Straight line models, 1.3.4 Coordinate geometry of a circle, 1.3.5 Centre and radius by completing the square, 1.3.6 Circle properties, 1.3.7 Parametric equations of curves (A-level only), 1.3.8 Parametric equations in context (A-level only), and 1.3 Coordinate Geometry in the x-y Plane. Each one has a worked solution and a mark scheme showing where the marks go.