Conic section theorems

Conic sections are shapes formed when a plane cuts through a cone at different angles, producing circles, ellipses, parabolas, or hyperbolas. Theorems about these shapes relate their properties—for example, in an ellipse, the sum of distances from any point on the ellipse to two fixed points (foci) is constant. Parabolas have a focus and directrix, where any point on the parabola is equidistant from both. Hyperbolas feature two foci with the difference of distances to any point on the hyperbola being constant. These properties help understand their geometric behavior and equations.