Algebra › Section K · Conics › Topic K.4
Hyperbolas
Change the ellipse's sum to a difference and the closed oval shatters into two infinite branches - the hyperbola, last of the four conic sections, and the only one with asymptotes it chases forever without touching.
In this topic
- The difference definition
- Anatomy and the two axes
- Standard form and orientation
- Asymptotes: the guiding box
- Worked example: opening left and right
- Worked example: standard form first, opening up and down
- Hyperbolas away from the origin
- Worked example: completing the square
- Identifying conics by equation
- Common mistakes to avoid
- Key takeaways
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