Name: 1. (a) Suppose that the conic sections Matric No.: C d r = and r = 1+ cos 0 1- cos intersect, where c and d are constant. Prove that they always intersect at right angles. (b) Consider the conic section given by 3 T = 1 cos # " (i) Write out, with justification, the directrix, the vertex (or vertices) and the focus (or foci) of the conic section. (ii) Determine the exact length of the curve of the conic section from 0 = π/3 to 0 = π/2. 2. Without using any web tools, sketch the following polar curves: (a) r2+ cos(30/2) (b) 72 = cos 20 Note: Use the graph of the polar equation in Cartesian coordinates for the sketching instead of plotting points, and provide all necessary angles and radius r in the sketching.

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