Director Circle of Parabola
Director circle is the geometric object related to the conic section and is defined as the locus of the intersection of the pair perpendicular tangent of any conic. For the parabola, the director circle is the directrix as all the perpendicular pairs of tangents of the parabola intersect each other at the directrix.
Chord of Contact
Chord of contact of the parabola is a secant line joining the point of tangency for the tangents drawn from the external point on the parabola. For parabola y2 = 4ax, chord of contact is given by T = 0, where T = yy1 – 2a(x + x1).Therefore the equation of chord of contact is given
T = yy1 – 2a(x + x1) =0
Where, (x1, y1) is the external point from which both the tangents are drawn to the parabola.
Parabola – Graph, Properties, Examples & Equation of Parabola
Parabola is one of the conic sections in Math. It is an intersection of a surface plane and a double-napped cone. A parabola is a U-shaped curve that can be either concave up or down, depending on the equation. Parabolic curves are widely used in many fields such as physics, engineering, finance, and computer sciences.
In this article, we will understand what is a Parabola, its graph, Parabola properties, Parabola examples, and equation of parabola in detail below.
Table of Content
- What is Parabola in Maths?
- Parabola Definition
- Parabola Shape
- Parabola Equation
- Properties of Parabola
- Standard Equation of Parabola
- Important Terms Related to Parabola
- Derivation of Parabola Equation
- Graph of Parabola
- Position of Point Relative to the Parabola
- Intersection with Straight Line
- General Equations of Parabola
- Parametric Coordinates of a Parabola
- Equation of Tangent to a Parabola
- Equation of Tangent in Point Form
- Equation of Tangent in Parametric Form
- Equation of Tangent in Slope Form
- Pair of Tangent from an External Point
- Director Circle of Parabola
- Chord of Contact
- Equation of Normal to a Parabola
- Equation of Normal in Slope Form
- Equation of Normal in Point Form
- Equation of Normal in Parametric Form
- Parabola Formulas
- Parabola Solved Examples
- Practice Questions on Parabola