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Cyberpunk Math Lab: The Non-Linear World FREE

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Conic Sections Introduction

60 min Cyberpunk Math Lab: The Non-Linear World

Learning Objectives

  • Identify parabolas, circles, ellipses
  • Understand focus and directrix
  • Graph basic conics

Key Concepts

Parabola

Set of points equidistant from focus and directrix

Ellipse

Set of points where sum of distances to two foci is constant

Theory

**Conic sections** are curves formed by slicing a cone: - **Circle:** x² + y² = r² (slice perpendicular to axis) - **Ellipse:** x²/a² + y²/b² = 1 (angled slice) - **Parabola:** y = ax² (slice parallel to side) - **Hyperbola:** x²/a² - y²/b² = 1 (steep slice) **Parabola focus:** For y = (1/4p)x², focus at (0, p)

Examples

Identify: x² + y² = 25

Solution: Circle centered at origin, radius 5