Page 07 MARKS 14. Find the particular solution of the differential equation 2 2 6 d y dy dx dx − + 9 y = 8 sin x + 19 cos x given that y = 7 and 1 2 dy dx = when x = 0. 15. (a) A beam of light passes through the points B(7, 8, 1) and T(-3, -22, 6). Obtain parametric equations of the line representing the beam of light. (b) A sheet of metal is represented by a plane containing the points P(2, 1, 9), Q(1, 2, 7) and R(-3, 7, 1). Find the Cartesian equation of the plane. (c) The beam of light passes through a hole in the metal at point H. Find the coordinates of H. 16. On a suitable domain, a curve is defined by the equation 2 2 4 9 36 x y + = . A section of the curve in the first quadrant, illustrated in the diagram below, is rotated 360° about the y-axis. y x 0 Calculate the exact value of the volume generated. [Turn over for next question 10 2 4 3 5