MathLab with Mr. Ahmed

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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11.6 Polar Equations of Conics

Focus on classify a conic and hyperbola eccentricity.

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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.

01Eccentricity and typeWorked steps · five questions02Writing a polar equation of a conicWorked steps · five questions
Lesson brief and rules

11.6 Polar Equations of Conics

In r=ed1+ecos⁡θ,er=\frac{ed}{1+e \cos \theta }, e is eccentricity: 0011 hyperbola.

Worked example 11
01 / Classify a conic with eccentricity 37\dfrac{3}{7}.
02 / Because 0<37<10<\dfrac{3}{7}<1, it is an ellipse.
03 / Answer: Ellipse
Worked example 2 · Hyperbola eccentricity

Classify a polar conic with e=4e=4.

e=4>1e=4>1, so the conic is a hyperbola. Answer: Hyperbola

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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