A family of parametric curves is given by the equations 3 = bmt] coa[bt], y = bain] aint}, t E [D31]. Some members of the family can be seen using this GeoGebra applet {In case the link doesn't open: wvnv.geogebra.orgfmfsdbyk29t} a) [2 points] For the curve given by b = 2, nd the equation of the tangent line when t = sryl'. b] [2 points] For the curve given by b = 21 nd all values of t E {l}, 211] for I.vhich the tangent line to the curve is vertical. c} {3 points] Find the length of the curve given by b = 3. [You may use a computer to evaluate the integral, but it can be done by hand.) cl} [2 points] Find the area enclosed by the curve given by b = 4. {You may use a computer to evaluate the integral, but it can be clone by hand.) e) ['I point} Using the applet, when in: is an integer, can you guess a formula, in terms of b, for the number of points where the curve is not smooth? [tour formula should work for both positive and negative values of b.)