Please solve this problem

(3) The Golden Gate Bridge has a main span of 4,200 feet and two main cables that hang down 500 feet from the top of each tower to the roadway in the middle. A parabola with vertex (h, k) can be parametrized using t) = (t, (t _ W + k) a, where a is a constant. Notice that rFlt) can be viewed parametrically as (t '02 a. If we combine those equations we get the more familiar equation _ (m h)2 a +k'. $=t and 3,): +19: y (a) Verify that 500 2 = 2100 _ t g 2100 is a parameterization of the cable across the main span. (b) Come up with a different parametrization of the same cable, in which the mid- point of the cable corresponds to t = 2100. (c) Find the length of the cable. Use the parameterization from part (a). To evaluate the denite integral for the arc-length, make the substitution t = 4410 tan 6. Use the trigonometric identity sec2 6 = 1 + tan2 I9 and 1 1 fsec3(a:) d3: = E secxtana: + Elnlsecx + tan$| + C. (d) Should the answer depend on the parameterization? Would you get a different answer if you used the parameterization from part (b)