Section D: Challenging Questions 1. Without actually nding the points of intersection, show that the parabola y2 = 4 px and the ellipse 2x2 + 3:2 = 6 intersect at right angles at (a, b). 2. Find the point on the parabola y = x2 that is nearest to the point (6,3). 3. A wooden beam has a rectangular cross section of height h and width w. The strength S of the beam is directly proportional to the product of the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter 50 cm