0Conic sections, in the context of JEE (Joint Entrance Examination), are curves formed by the intersection of a plane and a double-napped right circular cone. These curves, namely circles, parabolas, ellipses, and hyperbolas, are fundamental in mathematics and have wide applications in physics and engineering. Understanding their equations, properties, and relationships is crucial for JEE aspirants
Important Terms in Conic Sections
(1) Directrix: The fixed straight line is called the directrix of the conic section.
(2) Focus: The fixed point is called the focus of the conic section.
(3) Eccentricity: The constant ratio is called the eccentricity of the conic section and is denoted by e. If e>1, => hyperbola, e = 0 => circle, e = 1 => parabola and e <1 => ellipse.
(4) Axis: It is the straight line passing through the focus and perpendicular to the directrix. A conic is always symmetric about its axis.
(5) Latus rectum: It is the chord passing through the focus and perpendicular to the major axis and also includes both endpoints on the curve.
(6) Vertex: It is the point of intersection of the conic section and the axis.
(7) Focal chord: A chord passing through the focus of the conic.
(8) Focal distance: It is the distance of any point on the conic from the focus.
(9) Double ordinate: The double ordinate of a conic is a chord perpendicular to the axis.
Classification of Conic Section from Its Equation
The equation of conics represented by the second-degree equation can be written as ax2+2hxy+by2+2gx+2fy+c = 0. Here, ∆ = abc + 2fgh – af2 – bg2 – ch2. ∆ is the discriminant. We use this discriminant to determine the type of the conic section represented by the equation.
