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**Circles Write an equation given points**

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Example 1 Write the Equation of a circle with center (2,4) and containing the point (8,12) Use the Distance Formula to find the radius.

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Example 2 Write the Equation of a circle with the ends of a diameter at: (2, 16) and (–2, –2) Use the Distance Formula to find the radius. Use the Midpoint Formula to find the center.

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**Write Equation of a Circle given a Tangent**

Tangent is a line in the same plane as the circle that intersects the circle at exactly one point. Tangent to a circle is perpendicular to the radius at the point on tangency.

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Example 3 Write the equation of the line that is tangent to the circle at the given point. 1. Identify the center and the radius of the circle center is (0,0) radius r = 5 Find the slope of the radius at the point of tangency and the slope of the tangent. use (0,0) and (3,4)

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**The slope of perpendicular lines are negative reciprocals so the slope of the tangent is**

3. Find the slope-intercept equation of the tangent by using the point (3,4) and the slope

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**Example 4 Write an equation of a circle with the center (1, -8) and Tangent to x=8. **

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Example 5 Write the equation of the line that is tangent to the given circle at the given point. center radius Use (5,-5) and (1,-2) to find the slope of the radius. Find the slope-intercept equation of the tangent by using the point (5, -5) and the slope

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Example 6 Write the equation of a circle if its Center lies in the third quadrant and it is Tangent to x=-4 y=-2 This is the Axis of Symmetry Line Shows the diameter is 10 So the Radius is 5 y=-12

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Example 7 Write the equation of the line that is tangent to the given circle at the given point.

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Example 8 Write the equation of the line that is tangent to the given circle at the given point.

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Example 9 Write the Equation of a circle with the ends of a diameter at: (11, –8) and (–7, –8) Use the Distance Formula to find the radius. Use the Midpoint Formula to find the center.

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Example 10 Write the Equation of a circle with center (–3,5) and containing the point (9,10) Use the Distance Formula to find the radius.

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Example 11 Write the Equation of a circle with center (5, –2) and containing the point (–7,3) Use the Distance Formula to find the radius.

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