Question

Find equations of the tangent line and the normal line to the curve y = x^ 2−1/ x^ 2+x+1 at the point (1,0).

Answer 1

Step 1:

The equation is .

Apply derivative on each side with respect to .

Apply quotient rule .

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 .