3. Parametric Curves (7 marks total) (a) Explain inyour own words the similarities and differences between thefollowing two parametric curves. i. x = t 2 , y = t 4 ii. x = cost,y = cos2t (b) . Consider the curve defined parametricallyby x = at2 + bt and y = ct3 + dt2 + et, where a, b, c, d, e are allconstants. Give one example of what each of the constants a, b, c,d, e could equal so that your curve has exactly one verticaltangent line and no horizontal tangent lines. Show all of yourwork! Hint: start by finding a formula for dy dx !
