Conic sections are the curves obtained by intersecting a right circular cone with a plane. They include circles, ellipses, parabolas, and hyperbolas.
The set of all points in a plane that are at a fixed distance (radius r) from a fixed point (center h,k).
The set of all points equidistant from a fixed line (directrix) and a fixed point (focus).
Standard form (opening right): y² = 4ax. Focus: (a, 0). Directrix: x = -a. Latus Rectum: 4a.
The set of points where the sum of distances from two fixed points (foci) is constant.
Standard form: (x²/a²) + (y²/b²) = 1.
Eccentricity (e): c/a. For ellipse, e < 1.
Relation: c² = a² - b².
Length of Latus Rectum: 2b²/a.
The set of points where the difference of distances from two fixed points (foci) is constant.
Standard form: (x²/a²) - (y²/b²) = 1.
Eccentricity e > 1. Relation: c² = a² + b².