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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11.2 Ellipses

Focus on ellipse vertex and ellipse center.

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 an ellipseWorked steps · five questions02Equation of an ellipse from its featuresWorked steps · five questions
Lesson brief and rules

11.2 Ellipses

For x2a2+y2b2=1\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 with a>b>0a>b>0, 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, with 4>34>3.
02 / The larger denominator lies under x2x^{2}, so the horizontal semimajor axis is 44.
03 / Answer: (4,0)(4, 0)
Worked example 2 · Ellipse center

Find the center of x236+y216=1\dfrac{x^{2}}{36}+\dfrac{y^{2}}{16}=1.

No horizontal or vertical shifts appear. Answer: (0,0)(0,0)

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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