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Advanced Algebra Trigonometry Appendix B Objective: SWBAT graph and learn about the equations of circles

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Definition of a Circle A circle is a set of points a given distance from one point called the center. The distance from the center is called the radius.

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Circle 2-7-6-5-4-3-21573 0468 Below is a circle with radius 3 with the center at the origin. To find the equation of this circle, we let (x,y) be any point on the circle. Use the distance formula to plug in the information we know D = (x, y) ( x 1, y 1 ) = ( 0, 0 ) ( x 2, y 2 ) = ( x, y ) * The distance equals the radius 3. *

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Equation of a Circle The center of a circle is given by (h, k) The radius of a circle is given by r The equation of a circle in standard form is (x – h) 2 + (y – k) 2 = r 2

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Finding the Equation of a Circle If you have the center and the radius of the circle, plug it into the equation. Center = (h, k) = ( 3, 6 ) radius = 4 ( x - h )² + ( y – k )² = r² ( x - 3 )² + ( y – 6 )² = 4² ( x - 3 )² + ( y – 6 )² = 16

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Finding the Equation of a Circle Find the equation of a circle with: 1.Center = (h, k) = (-5, 0) radius = 8 2.Center = (h, k) = ( 3, 9) radius = 5 3.Center = (h, k) = ( -5, 3) radius = 2

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Graphing a Circle Graph the circle: ( x – 11 )² + ( y – 8 )² = 25

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Homework Page 450 # 49-54 (all)

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