Equations of Tangent and Normal to a Parabola
Here we list the equation of tangent and normal for different forms of parabola:

Equation of tangent to the parabola at is

Equation of normal to the parabola at is

If then equation of normal line is

The line touches the parabola
if

Equation of tangent to the parabola at is

Equation of normal to the parabola at is