Question

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

Answer 1

Step 1 :

The vector line equation is .

Where and .

The parametric equations of a line are

and .

Step 2 :

The parametric equations are and the point is .

Substitute the point in .

The point is corresponds to .

Apply derivative on each side with respect to t.

Substitute in above equation.

Write the vector notation in component form.

The equation of a tangent line passing through the point is

The parametric equations are and .

Solution :

The parametric equations are and .