1. Key Concept: Locus of Intersection of Perpendicular Tangents to a Parabola

For a parabola of the form ${y^2} = 4ax$, the locus of the point of intersection of any two perpendicular tangents is its directrix. The equation of the directrix for such a parabola is $x = -a$.

Why this concept is important: This property significantly simplifies problems involving perpendicular tangents. Instead of finding the equations of both tangents and then their intersection, we can directly use the directrix.

Brief Proof/Explanation: Let the equation of a tangent to the parabola ${y^2} = 4ax$ with slope $m$ be: $y = mx + \frac{a}{m}$ Suppose