Consider the Archimedian Spiral 1* = 20 + 3, 0 E [0, 2r] plotted below in black. The tangent to the spiral when 6 = 7r is plotted in blue. A parametric form of this spiral can be found by using t = 0 as the parameter: a(t) = [(3 + 2t) cos(t), (3 + 2t) sin(t)] . Find the point a,(11') = (-(3+2"Pi).0) I [E]. The Cartesian equation of the tangent to the curve at a(7r) is 9= [:II- The Cartesian equation of the normal to the curve at a,(7r) is v= :1\