MATHEMATICAL WORLD

PARABOLA 1. CONIC SECTIONS : A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed straight line. (a) The fixed point is called the FOCUS. (b) The fixed straight line is called the DIRECTRIX. (c) The constant ratio is called the ECCENTRICITY denoted by e. (d) The line passing through the focus & perpendicular to the directrix is called the AXIS. (e) A point of intersection of a conic with its axis is called a VERTEX. All Chapter Notes, Concept and Important Formula 2. GENERAL EQUATION OF A CONIC : FOCAL DIRECTRIX PROPERTY: The general equation of a conic with focus \((p, q) \) & directrix \(\mathrm{lx}+\mathrm{my}+\mathrm{n}=0\)   is :  \(\left(1^{2}+\mathrm{m}^{2}\right)\left[(x-\mathrm{p})^{2}+(\mathrm{y}-\mathrm{q})^{2}\right] \) \(=e^{2}(\mathrm{l} \mathrm{x}+\mathrm{m} y+\mathrm{n})^{2}  \) \(\equiv \mathrm{ax}^{2}+2 \mathrm{~h} ...