The equation is and points are and .

The equation is .

Apply derivative on each side with respect to .

.

.

Consider the point .

The derivative of the equation at the point is the slope of the line.

.

The line equation is .

Substitute and in the line equation.

The tangent line equation is .

Normal line is perpendicular to tangent line then,

slope of tangent line  slope of normal line is equal to .

Let slope of the normal as .

Therefore, .

.

point slope form of line equation is .

Substitute and in the above equation.

The normal line equation is .

The equation is .

Apply derivative on each side with respect to .

.

.

Consider the point .

The derivative of the equation at the point is the slope of the line.

.

The line equation is .

Substitute and in the line equation.

The tangent line is .

Normal line is perpendicular to tangent line then,

slope of tangent line  slope of normal line is equal to .

Let slope of the normal as .

Therefore,

.

point slope form of line equation is .

Substitute and in the above equation.

 The normal line equation is  .

Graph:

Graph the conic equation .

Graph the tangent line equations and .

Graph the normal line equations  and .

A the point :

The tangent line equation is .

The normal line equation is .

As the point :

The tangent line is .

 The normal line equation is  .

Graph:

Graph of the conic equation , the tangent line equations and and the normal line equations  and is

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