Question

Find equations of the tangent line and normal line to the

curve at the given point.

Answer 1

Step 1:

The equation of the curve is .

Apply derivative on each side with respect to .

                      ( Since )

Simplify the expression.

Substitute in above equation.

This is the slope of tangent to the curve at a point .

.

Step 2:

Find the tangent line using the point slope form : .

Where is the slope.

Substitute the values and in point slope form.

.

Step 3:

The normal and tangent lines are perpendicular to each other.

If is the slope of a tangent line then is the slope of a normal line.

Find the normal line using the point slope form : .

Substitute the values and in point slope form.

.

Solution :

The tangent line equation is .

The normal line equation is .