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

.