The equation of ellipse is  and  the point is  .

Normal line is perpendicular to the tangent line.

Slope of the tangent is derivative of the ellipse at certain point.

.

Differentiate on each side with respect to .

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If  is the slope of the tangent line then  is the slope of the normal line.

Slope of the normal line is

Slope of the normal at :

Point- slope form of line equation: .

Substitute  and  in above formula.

Equation normal  is .

The normal line and function are equal at a particular point.

Hence equate the function and the normal line equation.

Substitute  in .

.

Second point is .

(b)

Graph:

Graph the ellipse with normal line.

(a)

The second point is .

(b)

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