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10.6 Equations of Circles Advanced Geometry

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What do you need to find the equation of a circle? Coordinates of the Center of the circle. Radius – Distance from center to a point on the circle

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Let’s Look at a Circle

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Break it Down Given: Center is (h,k), the radius is r, and (x,y) is a point on the circle. The distance between (x,y) and (h,k) is r… so let’s use the distance formula.

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Break it Down

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Standard Equation of a Circle (x – h)² + (y – k)² = r² Where the center is at (h,k) & The radius is r

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Example Write the standard equation of a circle that has a center at the origin and a radius of 5.

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Example Write the standard equation of a circle with center (-5, 0) and radius 4.8.

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Example The point (2,1) is on a circle whose center is (4,-3). Write the standard equation of the circle.

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Example The point (0, -1) is on a circle whose center is (-4, 1). Write the standard equation of the circle.

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Graphing The equation of a circle is (x + 2)² + (y – 3)² = 9. First find the center and the radius of the circle, and then graph the circle.

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Graphing Graph (x – 3)² + (y + 1)² = 4

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Applying Graphs of Circles The equation of a circle is (x – 13)² + (y – 6)² = 9. Three points are located as follows: A(5, 6), B(14, 8), and C(20, 9). Which point is in the circle?

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