Question

 Find an equation of the tangent(s) to the curve at the given point. Then graph the curve and the tangent(s).

Answer 1

Step 1 :

The parametric equations are , and the point is .

Let the point is , then .

Step 2 :

Consider .

Differentiate the above equation with respect to t .

.

Consider .

Differentiate the above equation with respect to t .

.

The slope(m) of the tangent line is .

The slope(m) of the tangent line at :

.

Step 3 :

Point-slope form of a line equation .

Substitute the point and in the above equation.

The tangent line is .

Step 4 :

The graph of the curve and the tangent line is :

Solution :

The tangent line is .

The graph of the curve and the tangent line is :