What is directrix in conic section?

In conic sections, the directrix is a fixed straight line used to define and describe the shape of a conic curve such as a parabola, ellipse, or hyperbola.

 Explanation:

• The directrix helps in understanding the position and nature of the conic section.

• According to the locus definition, a conic section is the set of all points (P) in a plane that are at a constant ratio (called eccentricity, denoted by e) of their distance from a fixed point (focus) and a fixed straight line (directrix).

• Mathematical Condition:
  For any point P on the conic,
  Distance (P to Focus) / Distance (P to Directrix) = e

 Examples:

• In a parabola, e = 1, meaning the distance from the focus and the directrix is always equal.

• In an ellipse, e < 1, so points are closer to the focus.

• In a hyperbola, e > 1, meaning points are closer to the directrix than to the focus in certain regions.