If x=a (Cos(t) +t^2) and y=a (Sin(t) +t^2+t^3) then dy/dx equals to?

Answer 1

dx/dt = a(-sint + 2t)...............(i)

dy/dt = a(cost + 2t + 3t²).......(ii)

(ii) / (i) gives (dy/dt) / (dx/dt) = dy / dx = {a(cost + 2t + 3t²)} / { a(-sint + 2t)}

= (cost + 2t + 3t²) / (-sint + 2t)

Answer 2

dy/dx = (dy/dt)/(dx/dt) = (3t² + 2t + cos(t))/(2t - sin(t))