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MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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11.3 Hyperbolas

Focus on hyperbola vertex and hyperbola orientation.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Features of a hyperbolaWorked steps · five questions02Equation of a hyperbola from its featuresWorked steps · five questions
Lesson brief and rules

11.3 Hyperbolas

For x2a2−y2b2=1\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1, vertices are (±(\pm a,0)0).

Worked example 11
01 / Find a right vertex of x216−y29=1\dfrac{x^{2}}{16}-\dfrac{y^{2}}{9}=1.
02 / The transverse axis is horizontal and a=4a=4.
03 / Answer: (4,0)(4, 0)
Worked example 2 · Hyperbola orientation

Does y236−x216=1\dfrac{y^{2}}{36}-\dfrac{x^{2}}{16}=1 open horizontally or vertically?

The positive squared term is y2y^{2}. Answer: Vertically

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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