Condition for a Point to Lie Inside or Outside a Parabola

Condition for a Point to Lie Inside or Outside a Parabola

For:

$$y^2=4ax$$

define:

$$S=y^2-4ax$$

Then:

$$S<0\Rightarrow\text{point lies inside the parabola}$$

$$S=0\Rightarrow\text{point lies on the parabola}$$

$$S>0\Rightarrow\text{point lies outside the parabola}$$

Usage

- Used to determine the position of a point relative to a parabola.