this is the question: Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point (5, 25/2, 125/6)

The only problem is finding out how to parametrize. apparently x=t, but why???

Question

this is the question: Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point (5, 25/2, 125/6)

The only problem is finding out how to parametrize. apparently x=t, but why???

anonymous · Answer

you can choose y = t or z = t or x = t^2 ... x = t apparently makes the problem easiest but that's not the only choice. So if you make x = t then y = x^2/2 = t^2/2 and z = xy/3 = t^3/6. then you can proceed with the formula to calculate arc length.

nipunmalhotra93 · Answer

I disagree. You CANNOT choose y=t. That's because in $$x^2=2y, $$, x ranges from -inf to +inf. Choosing y=t will give you either +ve x or -ve x. We need to vary x over the whole real line. On the other hand, y ranges from 0 to inf. So, you have to choose x=t so that $$y=t^2/2$$ which satisfies the domain of y for the equation.