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Circles Write an equation given points. Example 1 Write the Equation of a circle with center (2,4) and containing the point (8,12) Use the Distance Formula.

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Presentation on theme: "Circles Write an equation given points. Example 1 Write the Equation of a circle with center (2,4) and containing the point (8,12) Use the Distance Formula."— Presentation transcript:

1 Circles Write an equation given points

2 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.

3 Example 2 Write the Equation of a circle with the ends of a diameter at: (2, 16) and (–2, –2) 1.Use the Midpoint Formula to find the center. 2.Use the Distance Formula to find the radius.

4 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.

5 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 2.Find the slope of the radius at the point of tangency and the slope of the tangent. use (0,0) and (3,4)

6 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

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

8 Example 5 Write the equation of the line that is tangent to the given circle at the given point. centerradius 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

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

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

11 Example 8

12 Example 9 Write the Equation of a circle with the ends of a diameter at: (11, –8) and (–7, –8) 1.Use the Midpoint Formula to find the center. 2.Use the Distance Formula to find the radius.

13 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.

14 Example 11 Write the Equation of a circle with center (5, –2) and containing the point (–7,3)


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