Translation:We consider the functionz = f(x, y) = x^2 + 16y^2 + 4.(a) Find the domain and range of f. Briefly justify your answer.(b) Draw the contour lines k = f(x,y) for k = 4 and k = 20.Show your work and indicate the value of k corresponding to each level curve on your figure. Don't forget the scales on the coordinate axes, and choose the scales so that the curves can be properly drawn and seen.(c) Draw the trace of f in the xz plane.(d) Find the directional derivative of f at the point (x, y) = (5, 1) in the direction of vector v = ?4, 3?.Show off all your hard work!