T. A cooling tower for a power plant is to be constructed in the shape of a hyperboloid of one sheet. 1:2 f :12 + gig/b? 2:2 {c2 = 1. The diameter of the circular base is l2(lm and the minimum diameter. 240m above the base. is 9(lm. (a) Sketch the tower. Where is the origin? (b) Find an equation for the tower, that is, nd [11-541 (c) Find the vector equation of a line (or two) inside the surface and passing through the point (11,030). Also sketch the line. Him: the equation should have the form (:17, y, z) = (a, CI: H) + t(d._ e, f): nd if, e, f such that the equation of the hyperboloid is satised for all t