Page 3 - LESSON NOTES

Parabola

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.

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.

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.