10.3 circles

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10.3 circles

  1. 1. Definition of a Circle All points on a circle are equidistant from thecenter of the circle. The distance between the center and anypoint on the circle is the radius.
  2. 2. Equation of a Circle Can be derived from the distance formula. Only for circles with center at (0, 0)!
  3. 3. Graphing Circles1. Write in standard form.2. Find the radius.3. Plot four intercepts r units from the origin.4. Connect with a circle.Example:Graph
  4. 4. Your Turn! Graph
  5. 5. Writing Equations1. Use the distance formula to find r.2. Plug it into standard form equation.Example:The point (1, 4) is on a circle centered at(0,0). Write the equation of the circle.
  6. 6. Your Turn! The point (5, 1) is on a circle centered at(0,0). Write the equation of the circle.
  7. 7. Tangent Lines A line is tangent to a circle if it touches thecircle at one point and is perpendicular tothe radius.
  8. 8.  To find the equation:1. Find the slope of the radius through thegiven point.2. Find slope perpendicular to that (opp.reciprocal)3. Use point-slope form to write equation.
  9. 9. Example Write an equation of the line tangent to thecircle at (2, 3).
  10. 10. Your Turn! Write an equation of the line tangent to thecircle at (-2, 4).

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