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Math Help - Arc Length and Curvature (3D vectors)

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    Arc Length and Curvature (3D vectors)

    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).

    My instructor told us to put those equations in parametric form so we could use the arc length formula, but I am not sure how to put those in that form.

    I know that these are the equations I must use, but how do I solve for t from the 2 equations I'm given??
    x = x_o - at
    y= y_o - bt
    z = z_o - ct
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    Quote Originally Posted by acg716 View Post
    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).

    My instructor told us to put those equations in parametric form so we could use the arc length formula, but I am not sure how to put those in that form.

    I know that these are the equations I must use, but how do I solve for t from the 2 equations I'm given??
    x = x_o - at
    y= y_o - bt
    z = z_o - ct
    I assume x2 means x^2, that is, x^2 ....

    The curve of intersection is found by solving x^2 = 2y and 3z = xy simultaneously. Let x = t. Then:

    x = t, y = \frac{t^2}{2} and z = \frac{t^3}{6}.

    Substitute into the usual arclength formula and do the calculation. Since you're integrating from the point where x = 0 to the point where x = 5 the integration limits should be obvious.
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