Conics - Important Definitions

CONICS - IMPORTANT DEFINITIONS

Mathematically, Conic is defined as the locus of a point moving in a plane in such a way that the ratio of its distance from a fixed point to a fixed straight line is always constant. The fixed point is known as 'Focus' and the fixed line is known as `Directrix' showndo in Fig. 6.2. 

The ratio of distance of the moving point from focus to the distance from directrix is known as eccentricity, represented by the do nollee ol letter 'e'.

In fig. 6.2, r1, r2 and r3 are the distances of moving point from focus and X1, X2 and X3 are the distances of moving point from directrix.

⸫ Eccentricity, e = Distance of the moving point from Focus / Distance of the moving point from the Directrix

Mathematically, the conic sections can be classified according to the value of eccentricity.

If eccentricity, e < 1, the curve obtained is Ellipse.

If eccentricity, e = 1, the curve obtained is Parabola.

If eccentricity, e > 1, the curve obtained is Hyperbola.

Ellipse, Parabola and Hyperbola are graphically represented by their eccentricity as shown in Fig. 6.3.