JEE Main 2018
Conic Sections
Parabola
Easy
Question
If two tangents drawn from a point to the parabola are at right angles, then the locus of is
Options
Solution
1. Key Concept: The Director Locus (Directrix) of a Parabola
For any conic section, the locus of the point of intersection of two tangents that are perpendicular to each other is known as its director locus.
- For a circle, it's called the director circle.
- For an ellipse, it's called the director circle.
- For a hyperbola, it's called the director circle.
- Crucially, for a parabola, the director locus is its directrix.
This is a standard and very important result that JEE aspirants should commit to memory, as it often provides a shortcut to solving problems like this one.
2. Standard Equation of a Parabola and its Directrix
The standard