Conic Sections
Circles, ellipses, parabolas, and hyperbolas
Start with the basics and progress through 9 lessons. Each lesson builds on the previous one.
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In This Topic (9 lessons)
Introduction to Conic Sections
Learn what conic sections are and how slicing a cone creates circles, ellipses, parabolas, and hyperbolas.
Introduction to Ellipses
Learn what an ellipse is, its key features, and the standard form equation.
Parabolas in Vertex Form
Learn to write, graph, and analyze quadratic functions in vertex form y = a(x - h)² + k.
Circles in Standard Form
Learn how to write and interpret the equation of a circle in standard form.
Ellipses in Standard Form
Learn to write, graph, and analyze ellipses using the standard form equation.
Introduction to Hyperbolas
Learn what hyperbolas are, their key features, and how they differ from other conic sections.
Circles in General Form
Learn to convert between general and standard form of circle equations and find center and radius.
Hyperbolas in Standard Form
Learn to write and graph hyperbolas in standard form, identify key features like center, vertices, foci, and asymptotes.
Identifying Conic Sections
Learn to distinguish between circles, ellipses, parabolas, and hyperbolas from their equations.
Conic sections are curves formed by intersecting a cone with a plane: circles, ellipses, parabolas, and hyperbolas. These curves appear throughout mathematics, physics, and engineering.
What You'll Learn
- Identify types of conic sections
- Graph circles and ellipses
- Graph parabolas and hyperbolas
- Write equations in standard form
- Apply to real-world problems
Frequently Asked Questions
What are the four conic sections?
Circle, ellipse, parabola, and hyperbola. Each is formed by slicing a cone at different angles.
Where do conics appear in real life?
Planetary orbits (ellipses), satellite dishes (parabolas), bridge arches, and navigation systems.
How do I identify the conic from its equation?
Look at the squared terms: both x² and y² with same sign/coefficient = circle or ellipse; different signs = hyperbola; only one squared term = parabola.