Pre-Calculus

Pre-Calculus prepares students for calculus by covering functions, trigonometry, and analytical geometry.

Functions and Their PropertiesTrigonometric FunctionsAnalytical Geometry
Polynomial and Rational FunctionsExponential and Logarithmic FunctionsConic Sections
Modeling Real-World DataEngineering and DesignFinance and Population Growth
Graphing TechniquesProblem-Solving and Test Preparation
Functions and Their ...Trigonometric Functi...Analytical GeometryPolynomial and Ratio...Exponential and Loga...Conic SectionsModeling Real-World ...Engineering and Desi...Finance and Populati...Graphing TechniquesProblem-Solving and ...
Advanced Topics

Conic Sections

Slices of a Cone: Circles, Ellipses, Parabolas, and Hyperbolas

Conic sections are the curves formed by slicing a double-napped cone at different angles. The four types are circles, ellipses, parabolas, and hyperbolas, each with unique properties and equations.

Main Types

  • Circle: All points equidistant from a center.
  • Ellipse: Like a stretched circle.
  • Parabola: The path of a thrown ball.
  • Hyperbola: Two open curves, like a satellite’s path.

Why Study Conics?

Conic sections appear in planetary orbits, satellite dishes, headlights, and architecture!

Examples

  • The shape of a planet’s orbit around the sun is an ellipse.

  • Satellite dishes use parabolic shapes to focus signals.

In a Nutshell

Conic sections are the curves formed from slicing a cone and have wide applications in science and engineering.

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Modeling Real-World Data