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Understanding Conic Sections: Circles and More

Learn about graphing conic sections including circles, parabolas, ellipses, and hyperbolas. Discover the standard form for a circle equation, finding center and radius. Practice problems included.

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Understanding Conic Sections: Circles and More

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  1. Circles – An Introduction SPI 3103.3.11    Graph conic sections (circles, parabolas, ellipses and hyperbolas) and understand the relationship between the standard form and the key characteristics of the graph.

  2. The general form for the equation of a circle is (x – h)2 + (y – k)2 = r2. • The center of the circle is the ordered pair (h, k). • The radius of the circle is r.

  3. For each of the following problems, find the center and radius. 1. (x + 3)2 + (y – 4)2 = 25

  4. 2. (x – 1)2 + y2 = 44 3. (x + 8)2 + (y + 2)2 = 7

  5. 4. x2 + y2 = 18 5. (x – 7)2 + (y + 2)2 = 0 6. x2 + (y – 4)2 = 44

  6. Write an equation for the circle with the given center and radius. 7. Center (2, –7), radius 4

  7. 8. C = (0, –2), r = 6 9. C = (0, 0), r =

  8. Write each equation in the form (x – h)2 + (y – k)2 = r2. 10. x2 + y2 – 10x + 6y – 13 = 0

  9. 11. x2 + y2 + 4x – 14y + 17 = 0 12. x2 + y2 + 20x + 247 = 0

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