4(a) Suppose a particle P is moving in the plane so that itscoordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t.
x2 y2
(i) By finding a, b ? R such that a2 + b2 = 1, show that P istravelling on an elliptical
path. [10 marks] (ii) Let L(t) be the distance from P to theorigin. Obtain an expression for L(t).[8 marks] (iii) How fast isthe distance between P and the origin changing when t = ?/8?[7marks]
(b) A wire of length 100 centimeters is cut into two pieces. Onepiece is bent to form a square. The other piece is bent to form anequilateral triangle. Find the dimensions of the two pieces of wireso that the sum of the areas of the square and the triangle isminimized.(25marks)
