The curve C C\,C has parametric equations
x=2t+1t+2\displaystyle x = \frac{2t + 1}{t + 2}x=t+22t+1, y=4t−1t+2\displaystyle y = \frac{4t - 1}{t + 2}y=t+24t−1, where 0≤t≤40 \leq t \leq 40≤t≤4
Show that C C\,C is part of a straight line.
Find the exact length of this line segment.
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.