Parabola

PARABOLA

Parabola is defined as a curve traced out by a point moving in a plane such that its distance from a fixed point called Focus is always equal to its distance from a fixed line called Directrix. ie., eccentricity of parabola is equal to one.

eccentricity e = Distance of the point from the Focus / Distance of the point from the Directrix

= Constant = 1 (unity)

Refering the fig. 6.13.

e = FP / PM = 1

⸫ PF = PM

and

AV = VF

The important terminologies of parabola are given below and shown in Fig. 6.14.

Focus : Fixed point about which locus of point (Parabola) is described. 

Directrix : Fixed straight line about which locus of point (Parabola) is described.

Abscissa (VF, VN): The distance along the axis between the vertex and a point on the axis.

Ordinate (LF, MN): A line drawn from any point on the curve and perpendicular to the axis.

Double Ordinate (LL', MM'): The ordinate extended to cut the parabola on the other side of the axis. Double ordinate is twice the length of the ordinate.

Latus Rectum (LL'): The double ordinate passing through the Focus.