Step 1:

The equation is .

Apply on each side with respect to .

.

Slope of the tangent line at .

.

Slope of the function is derivative of the function at that point.

Slope of the tangent line is .

Step 2:

Substitute in .

.

The tangent at the point .

Point slope form of line equation is .

Substitute and in the above equation.

Tangent line equation is .

The equation of normal line to at is . \ \

Where is slope of the tangent line.

Substitute and in the above equation.

Normal line equation is .

Solution:

Tangent line equation is .

Normal line equation is .

Step 3:

Equation of circle with center and radius is .

Differentiate on each side with respect to .

Substitute  .

Substitute in the above equation.

Step 4:

Substitute in the circle equation

Circle passes through the point .

Roots of the quadratic equation is .

Then,

Therefore and .

Substitute in .

Substitute in .

.

Step 5:

Graph:

Graph both the circle equations, curve and tangent line.