Key Concepts: Conic Sections (Intro) ⭐

What Are Conic Sections?

Curves formed by the intersection of a plane and a double cone: circle, ellipse, parabola, and hyperbola.

Overview

• Circle: plane is perpendicular to the axis of the cone.
• Ellipse: plane intersects at an angle, cutting through one nappe.
• Parabola: plane is parallel to one slant side of the cone.
• Hyperbola: plane intersects both nappes of the cone.

General Second-Degree Equation

Ax² + Bxy + Cy² + Dx + Ey + F = 0

Identify the conic by comparing A and C: if A = C → circle; if A ≠ C but same sign → ellipse; if A or C = 0 → parabola; if A and C have opposite signs → hyperbola.