Choose either theoretical Problem Problem 1 For all items, c is a constant. Each item specifies a disc or ellipse E. For each item, Xe (x, y) = c if (x, y) is in Ɛ, whereas Xɛ (x, y) = 0 if (x, y) is not in E. For each item, find an algebraic formula for [Rxɛ] (r, a) in terms of r, a, c, and parameters defining &. (1.1) For this item, & is the disc with radius S centered at (20, yo): where (x − x0)² + (y — yo)² ≤ S². (1.2) For this item, & is the ellipse centered at 0 where (x²/a²) + (y²/b²) ≤ 1. (1.3) For this item, &E is the ellipse centered at 0 with principal semi-axes of lengths a in the direction [cos(7), sin(y)] and b in the direction [-sin(y), cos(y)]. (1.4) For this item, & is the ellipse centered at (xo, yo) where [(x - xo)²/a²] + [(y — yo)²/b²] ≤1. (1.5) For this item, & is the ellipse centered at (xo, yo) with principal semi-axes of lengths a in the direction (cos(y), sin(y)] and b in the direction [-sin(y), cos(y)].