A sporting airplane is flying such that its height varies with time in accordance with the formula y = 10 + 3/(t0 + t)2, whereas its horizontal distance varies with time as x = (t0 + t)2, where t is in seconds, and x and y are in metres, t0 = 1 sec.

(a) Find the trajectory of the airplane y as a function of x.

(b) What is the function, describing the trajectory?

(c) Plot it accurately indicating asymptotes, if any.

(d) Find a position (coordinates) of the airplane after 5 sec. Round off your answer up to one decimal place.