(c) Find the matrix Q. (2) 7. The parabola has equation = 4ax, where is a positive constant. C y2 a The point 2at) is a general point on P(at2, C. (a) Show that the equation of the tangent to at 2at) is C P(at2, = + ty x at2 (4) The tangent to at meets the at a point C P y-axis Q. (b) Find the coordinates of Q. (1) Given that the point is the focus of S C, (c) show that is perpendicular to PQ SQ. (3) (a) Prove by induction, that for , 8. (6) (b) Hence, show that where and are integers to be found. a, b c (4) 9. The complex number is given by w = 10 5i w – (a) Find . (1) (b) Find arg giving your answer in radians to 2 decimal places w, (2)
(c) Find the matrix Q. (2) 7. The parabola C has equation y2 = 4ax, where a is a positive constant. The point P(at2, 2at) is a general point on C. (a) Show that the equation of the tangent to C at P(at2, 2at) is ty = x + at2 (4) The tangent to C at P meets the y-axis at a point Q. (b) Find the coordinates of Q. (1) Given that the point S is the focus of C, (c) show that PQ is perpendicular to SQ. (3) 8. (a) Prove by induction, that for , (6) (b) Hence, show that where a, b and c are integers to be found. (4) 9. The complex number w is given by w = 10 – 5i (a) Find . (1) (b) Find arg w, giving your answer in radians to 2 decimal places (2)
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