vector calculus

1. (a) Suppose that the conic sections C d 1 = 1 + cos 0 and r = 1 - cos 0 intersect, where c and d are constant. Prove that they always intersect at right angles. with calculations (b) Consider the conic section given by 3 r = 1 - cos 0 (i) Write out, with justification, the directrix, the vertex (or vertices) and the focus (or foci) of the conic section. with calculations (ii) Determine the exact length of the curve of the conic section from 0 = 7/3 to 0 = 7/2. with calculations