I am having trouble setting up the equations for the Mathematica. Please do a, b and c.

mmands for reference on future assignments. 1. A curve in R3can be described by a set of parametric equations of the form xf(t) y = g(t) z h(t) and similarly for a curve in R2 if we ignore the z component. Here the Mathematica commands are Parametriclotfiy), (t, taminy tmasx) and ParametricPlot3Df.f,.t, tmin tmax)1. For example, to plot part of a helix in R3, the command is given by ParametricPlot3DlfCos[t],Sin[t],t), (t, -10, 10]]. (a) (2 points) See the subsection labeled Using Computers to Draw Space Curves in Section 13.1. Here there is an example of a curve that lies on a torus. Now, a torus has equation given by where c is the distance from the center of the tube to the center of the hole of the torus and a is the radius of the tube. It turns out that the so-called (p, q)-torus knots are well- studied mathematical objects. The parameter p is the number of times the curve goes around the tube, and q is the number of times the curve goes around the larger circle (i.e. the number of times the curve goes around the z-axis). ot command to plot the surface of the torus with For this problem, use the appropriate pl c4 and a 1. Then, modify the example from the text and use the parametric plot command to plot a (3,5)-torus knot. To get both plots on the same graph, label each plot by pl and p2, and then run the Show/p1, p2] command. More explicitly, do p1="Some type of plot command here" and p2-ParametricPlot3D[ More commands here] and then Show[p1, p2]. For your write up, also include a sentence or two describing the situation. (b) (2 points) Plot the curve given by for 0 st s 1. The curve lies on a surface. Determine which surface it lies on and find an equation for that surface. For this problem, provide a single plot as in part (a) of both the surface and the parametric curve. Also, explain mathematically how you know the curve is on the surface. Make sure to use the Equation tool in Word (or whichever word editor you use) for all equations. points) Find parametric equations for curve of intersection of the cylinders given by the equations x2 +y2 4 and 2+24.For this problem, provide a single plot with both cylinders and the curve given by your parametric description. Also, describe how you obtained the parametric equations, again using the Equation tool as needed. (c) (2