Conic Sections

Points with equal distances from a fixed line and a fixed point

A parabola is the set of points in a plane that are equidistant from a fixed line (directrix) and a fixed point (focus).

y² = 4ax

This equation represents a parabola with vertex at origin, focus at (a,0), and opening to the right.

Points where the sum of distances from two fixed points is constant

An ellipse is defined as the set of points where the sum of distances from two fixed points (foci) remains constant.

x²/a² + y²/b² = 1

This equation represents an ellipse with center at origin, semi-major axis a along x-axis, and semi-minor axis b along y-axis.