Edexcel Mathematics June 2022 · Paper 2 · Question 16 · ExamRizz

ExamRizzEdexcel MathematicsMathematics

June 2022 · Paper 2 · Question 16 · 12 marks

16. y lPC O x Figure 6 Figure 6 shows a sketch of the curve C with parametric equations x = 2 tan t + 1 y = 2 sec2 t + 3 − 4π  t  3π The line l is the normal to C at the point P where t = 4π (a) Using parametric differentiation, show that an equation for l is y = − 1 2x + 17 2 (5) (b) Show that all points on C satisfy the equation y = 1 2 (x − 1)2 + 5 (2) The straight line with equation y = − 1 2x + k where k is a constant intersects C at two distinct points. (c) Find the range of possible values for k . (5) 45 46 47 48  