Geometry: An Interactive Journey to Mastery

The Equation of a Circle

Lesson 20

Topics
x The equation of a circle.
x Pythagorean triples.
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x The equation of a circle with center C ͼ௘a, b௘ͽDQGUDGLXVrLVͼ௘xía௘ͽ^2 ͼ௘yíb௘ͽ^2 = r^2 ͼ௘7KLVLVMXVWDQ
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Summary
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given radius. As a bonus, we explore an interesting connection to Pythagorean triples.
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The equation is x^2 ͼ௘yí௘ͽ^2 = 29^2 = 841. Noting that 20^2 ͼ௘í௘ͽ^2 = 20^2 + 21^2 = 400 + 441 = 841, we see that
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The radius of the circle is the distance between the two given points—namely, SS S^22  2.^2 Thus, the
equation of the circle is xy SSS^22 2.^22 That is,
xy SSS^22 2.^2