What is Directrix in Conic Section?
Answer: In a conic section, the directrix is a fixed-line used to define the geometric shape, and points on the conic section are equidistant from the focus (a fixed point on the conic section) and the directrix.
Explanation:
In a conic section, the directrix is a fundamental element that, along with the focus, helps define the shape of the conic section. The conic section can be a circle, ellipse, parabola, or hyperbola.
In a parabola, the directrix is a fixed straight line perpendicular to the axis of symmetry. All points on the parabola are equidistant from the focus (a fixed point on the parabola) and the directrix. This distance is called the focal length.
For ellipses and hyperbolas, the directrix is part of a larger construction involving the major and minor axes. The directrices for these conic sections are typically used in the context of defining the geometry and properties of the figure.
In the case of a circle, the concept of a directrix is not explicitly used, as all points on a circle are equidistant from the center.
Conclusion – What is Directrix in Conic Section?
The directrix is a line used in conic sections, such as parabolas, to define their geometric properties. For a parabola, the directrix is a line that is located outside the curve and is parallel to the axis of symmetry. It is equidistant from all points on the parabola. The distance from any point on the parabola to the directrix is equal to the distance from that point to the focus of the parabola. In essence, the directrix helps to determine the shape and orientation of the parabola.