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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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11.4 Shifted Conics

Focus on shifted center and shifted circle radius.

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Ideas in this lesson

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01Shifted conicsWorked steps · five questions02Identifying a conic by completing the squareWorked steps · five questions
Lesson brief and rules

11.4 Shifted Conics

In (x−h)2a2+(y−k)2b2=1\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1, the ellipse center is (h,k)(h,k).

Worked example 11
01 / Find the center of (x−4)29+(y+7)225=1\dfrac{(x-4)^{2}}{9}+\dfrac{(y+7)^{2}}{25}=1.
02 / Match (x−h)(x-h) and (y−k)(y-k): the center is (4,−7)(4,-7).
03 / Answer: (4,−7)(4, -7)
Worked example 2 · Shifted circle radius

Find the radius of (x−4)2+(y+6)2=64(x-4)^{2}+(y+6)^{2}=64.

The radius is the positive square root of 6464. Answer: 88

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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