Parabola

Definition 2 A parabola is the set of all points

in a plane that are equidistant from a fixed line

and a fixed point (not on the line) in the plane.



The fixed line is called the directrix of

the parabola and the fixed point F is called the

focus (Fig 11.13). (‘Para’ means ‘for’ and

‘bola’ means ‘throwing’, i.e., the shape

described when you throw a ball in the air).

$Note If the fixed point lies on the fixed

line, then the set of points in the plane, which

are equidistant from the fixed point and the

fixed line is the straight line through the fixed

point and perpendicular to the fixed line. We

call this straight line as degenerate case of

the parabola.

A line through the focus and perpendicular

to the directrix is called the axis of the

parabola. The point of intersection of parabola

with the axis is called the vertex of the parabola

(Fig11.14).

11.4.1 Standard equations of parabola The

equation of a parabola is simplest if the vertex



is at the origin and the axis of symmetry is along the x-axis or y-axis. The four possible

such orientations of parabola are shown below in Fig11.15.