The curve C C\,C has parametric equations
x=2t1+t2x=\dfrac{2t}{1+t^2}x=1+t22t, y=1−t21+t2y=\dfrac{1-t^2}{1+t^2}y=1+t21−t2, where t∈Rt\in\mathbb{R}t∈R.
Show that C C\,C lies on the circle x2+y2=1x^2+y^2=1x2+y2=1.
State, with a reason, the point on the circle which is not generated by any real value of ttt.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.