equation of tangent line and parametric equation of tangent line (are they equivalent)

Question

I am not sure about the steps to finding parametric equations of tangent lines and was wondering if these statements are equivalent

Is there a difference if I am asked to find:

• equations of tangent lines to the parametric curve at a given point
• parametric equations of tangent lines to the parametric curve at a given point

Answer 1

I believe that if you are asked to find the equation of a tangent line to parametric curves at a given point, it is likely that the writer of the question intends for you to give a single equation in terms of x and y, with no t.

If you are asked to find parametric equations of a tangent line to parametric curves at a given point, then your answer will involve two equations, one with x in terms of t and one with y in terms of t.