Circles Write an equation given points

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Presentation transcript:

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 to find the radius.

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.

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.

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)

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

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

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

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

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

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

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.

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.

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.