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 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 .

Graph:

Graph the conic equation .

Draw the tangent lines and .

Draw the normal lines and .

At the point :

The tangent line equation is .

The normal line equation is .

At the point :

The tangent line equation is .

The normal line equation is .

Graph :

Graph the conic equation , tangent lines and and the normal lines and .

.