Hyperbola Explained: Graphing, Asymptotes, Foci & Standard Form – Pre-Calc, Algebra I Conic Sections

Описание: In this lesson from the Mathsupport channel,    / @mathsupportnow   , we explore the conic section known as the hyperbola. You’ll learn the formal definition, how to identify key features like the center, vertices, transverse axis, conjugate axis, asymptotes, and foci, and how to graph hyperbolas both horizontally and vertically. This tutorial includes multiple examples and step-by-step guidance for sketching hyperbolas without technology.
What You’ll Learn:
✅ The locus definition of a hyperbola
✅ The difference between horizontal and vertical transverse axes
✅ How to identify and graph the center, vertices, and asymptotes
✅ How to use the standard form of a hyperbola equation
✅ How to find the distance to the foci using the Pythagorean relationship
✅ How to graph hyperbolas using a bounding box and asymptotes as guides

Who Benefits from this Video:
🎯 Grade 11–12 students learning conic sections (BC, Canadian, US curricula)
🎯 Pre-Calculus and Algebra II learners studying hyperbolas
🎯 College-prep and SAT/ACT learners practicing conic graphing
🎯 Parents and tutors supporting math learners
🎯 Anyone curious about how hyperbolas work and how to sketch them accurately

Timestamps:
00:00 – Introduction to Hyperbolas
00:12 – Locus Definition Explained
01:50 – General vs Standard Form of Hyperbola
02:22 – Center, Transverse Axis, Conjugate Axis
04:38 – Relationship Between a, b, and c (Foci Distance)
06:28 – Horizontal vs Vertical Hyperbolas
08:46 – Asymptote Equations Explained
09:01 – Example 1: Horizontal Hyperbola with Center at (0, 0)
10:33 – Graphing Vertices, Conjugate Axis, and Asymptotes
13:25 – Sketching the Hyperbola Curve
13:31 – Example 2: Vertical Hyperbola with Center at (1, –2)
16:44 – Graphing Vertices, Conjugate Axis, and Asymptotes
18:57 – Finding Foci Using a² + b²
19:08 – Summary & Key Takeaways

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