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Circles Learning goals:

Circles Learning goals:. Write the equation of a circle. Use the equation of a circle and its graph to solve problems. Graphing a circle using its four quick points. CIRCLES. What do you know about circles?. Definitions.

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Circles Learning goals:

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  1. CirclesLearning goals: • Write the equation of a circle. • Use the equation of a circle and its graph to solve problems. • Graphing a circle using its four quick points.

  2. CIRCLES What do you know about circles?

  3. Definitions • Circle:The set of all points that are the same distance (equidistant) from a fixed point. • Center: the fixed points • Radius:a segment whose endpoints are the center and a point on the circle

  4. The equation of circle centered at (0,0) and with radius r Solution: Let P(x, y) represent any point on the circle x 2 + y 2 = r 2

  5. Finding the Equation of a Circle The center is (0, 0) The radius is 12 The equation is: x 2 + y 2 = 144

  6. Write out the equation for a circle centered at (0, 0) with radius =1 Solution: Let P(x, y) represent any point on the circle

  7. Ex. 1: Writing a Standard Equation of a Circle centered at (0, 0) and radius 7.1 x 2 + y2 = r2 Standard equation of a circle. x 2 + y2 = 7.12 = 50.41 Simplify.

  8. Graphing Circles • If you know the equation of a circle, you can graph the circle • by identifying its center and radius; • By listing four quick points: the upmost, lowest, leftmost and rightmost points.

  9. Graphing Circles Using 4 quick points x 2+ y 2= 9 Radius of 3 Leftmost point (-3,0) Rightmost point(3,0) Highest point(0, 3) Lowest point(0, -3)

  10. Is the point on, inside or outside of a circle x 2 + y 2 = 9?

  11. Find the x and y intercepts algebraically.

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