Answer the following Vector Calculus problem. Be sure to answer the entire question. Thank you!

4. The double cone 2.r? = y' + 2 intersects the sphere x2 +y' + 22 = 12x -11 along two closed curves C, and C2. Let E be the portion of the cone with boundaries given by C1 and C2. Likewise, let E2 be the portion of the sphere with boundaries also given by C1 and C2. (a) (10 pts) Find parametrizations for C1 and C2 that has counter-clockwise orienta- tion about the r-axis. (b) (12 pts) Find a parametrization for E, and use it to determine the area of E1.(c) (12 pts) Find a parametrization for _2 and use it to determine the area of Ez . (d) (6 pts) Is En a portion of a graph of some function? Likewise, is _2 a portion of a graph of some function? (e) (10 pts) Compute the line integral [, F . ds = fox'dx - zdy + ydz for both C1 and C2 . Determine the value of Jo, F . ds - Jc, F . ds . (f) (5 pts) Does your answer in part (e) change if you replace a2 with f(x, y, z)