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CIRCLES

Learn how to write the equation of a circle given its center and radius length, and find the center and radius lengths given the equation. Also, practice finding the equation of a circle tangent to a given line and passing through a specific point.

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CIRCLES

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  1. CIRCLES Topic 10.2

  2. Definitions • Circle:The set of all points that are the same distance from the center • Radius:a segment whose endpoints are the center and a point on the circle

  3. Equation of a Circle

  4. Writing the Equation of a Circle • Group x terms together, y-terms together, and move constants to the other side • Complete the square for the x-terms • Remember that whatever you do to one side, you must also do to the other • Complete the square for the y-terms • Remember that whatever you do to one side, you must also do to the other

  5. Example: Write the equation and find the center and radius length of : Group terms Complete the square

  6. You try!!: Write the equation and find the center and radius length of :

  7. THINK ABOUT IT Find the center, the length of the radius, and write the equation of the circle if the endpoints of a diameter are (-8,2) and (2,0). Center: Use midpoint formula! Length: use distance formula with radius and an endpoint Equation: Put it all together

  8. THINK ABOUT IT • Write the equation of a circle whose center is (2, -1) and tangent to x = 6

  9. THINK ABOUT IT • Write the equation of a circle who passes through (-2, 3) and is centered at (2, -1)

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