Hyperbolas Complete Guide (Graphing, Writing Equations, Finding Asymptotes, Foci, Eccentricity)

Dive into the world of hyperbolas with this complete guide! We'll cover everything you need to know, from understanding what a hyperbola is to graphing them and writing their equations in standard form.

This video breaks down key concepts like vertices, foci, eccentricity, and asymptotes. You'll learn how to determine if a hyperbola opens horizontally or vertically and how to find its center, even when it's shifted from the origin. We'll also explore the relationship between 'a', 'b', and 'c' values using the Pythagorean-like theorem.

With 8 detailed examples, you'll gain practical experience in:

Graphing hyperbolas from their equations.
Writing the equations of asymptotes.
Converting general equations to standard form by completing the square.
Deriving the equation of a hyperbola given its vertices and foci or asymptotes.
Whether you're studying for an algebra, precalculus, or calculus course, this tutorial will help you master hyperbolas!

Timestamps:
0:00 - Introduction to Hyperbolas: Complete Guide
0:25 - What is a Hyperbola? Definition and Key Terms (Vertices, Foci)
1:30 - Standard Forms of Hyperbola Equations (Horizontal vs. Vertical Transverse Axis)
2:30 - Relationship between a, b, and c: c² = a² + b²
3:00 - Example 1: Graphing x²/4 - y²/9 = 1 (Center at Origin, Horizontal)
5:45 - Equations of Asymptotes (Rise over Run)
6:50 - Example 2: Graphing y²/1 - x²/4 = 1 (Center at Origin, Vertical)
9:40 - Understanding Eccentricity for Hyperbolas
11:00 - Example 3: Graphing (x+3)²/9 - (y-1)²/16 = 1 (Shifted Center, Horizontal)
14:00 - Equations of Asymptotes (Point-Slope Form with Shifted Center)
16:40 - Example 4: Graphing (y+2)²/4 - (x-2)²/25 = 1 (Shifted Center, Vertical)
19:50 - Example 5: Writing Standard Form and Graphing (Completing the Square)
24:30 - Example 6: Writing Standard Form (Completing the Square - Vertical)
27:50 - Example 7: Writing Equation from Vertices and Foci
31:00 - Example 8: Writing Equation from Vertices and Asymptotes
33:40 - Conclusion and Additional Resources

Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)
https://www.mariosmathtutoring.com/fr...

➡️JOIN the channel as a CHANNEL MEMBER at the "ADDITIONAL VIDEOS" level to get access to my math video courses(Algebra 1, Algebra 2/College Algebra, Geometry, and PreCalculus), midterm & final exam reviews, ACT and SAT prep videos and more! (Over 390+ videos)
   / @mariosmathtutoring