Problem 1 For all items, c is a constant. Each item specifies a disc or ellipse E. For each item, Xɛ(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 ε. (1.1) For this item, & is the disc with radius S centered at (xo, yo): where (x-xo)²+(y-yo)² <S². (1.2) For this item, & is the ellipse centered at 0 where (r2/a²) + (y²/62) ≤ 1. (1.3) For this item, Ɛ is the ellipse centered at 0 with principal semi-axes of lengths a in the direction [cos(y), sin(y)] and b in the direction [-sin(y), cos(7)]. (1.4) For this item, & is the ellipse centered at (xo, yo) where [(x - xo)2/a2] + [(y-yo)²/62] ≤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)].