The equation of parabola is .

The line equation is .

Change the line equation in Slope intercept form .

Comparing line equation with .

Slope of the line is  .

Since the required normal line is in parallel with given line, their slopes are equal.

Slope of the normal line is  .

Slope of a tangent line is derivative of the curve.

Differentiate on each side with respect to .

Slope of the tangent line is .

Tangent line is perpendicular to the normal line.

If the two lines are perpendicular then their slopes will be .

Here and

Find corresponding value with the curve.

If  , then

Hence the normal line exist at a point .

Equation of a normal line at point   with slope  .

Point slope form: .

Substitute and in the above formula.

Equation of the normal line is .