Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

My question is, do I simply solve for t (t=1) and then take a derivative of each? I'm confused on what it is asking for.

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- February 2nd 2010, 08:43 AMRhode963Parametric tangent line
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

My question is, do I simply solve for t (t=1) and then take a derivative of each? I'm confused on what it is asking for. - February 2nd 2010, 09:55 AMHallsofIvy
Well, it is asking for parametric equations of the tangent line!

You should know that if you are given a curve as (x(t), y(t), z(t)) then the derivative vector <x'(t), y'(t), z'(t)> is tangent to the curve. You should also know that parametric equations for a line through with "direction vector" <A, B, C> are , , and .

You are given the point and the "direction vector" of a tangent line is a tangent vector at that point. Differentiate x, y, and z with respect to t, evaluate at t= 1, and use that as the "direction vector" of the line. - February 2nd 2010, 10:15 AMRhode963
So and evaluated at t=1, , meaning the parametric tangent line is... ?