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Circles Learning goals:

Explore the fundamental concepts of circles, including how to write their equations and graph them effectively. Learn about the definitions of key terms like center and radius, and see examples of standard equations for circles centered at the origin. Discover how to graph circles using the center and radius, and identify key points to aid in visualization. Solve problems involving circles, such as determining if a point lies on, inside, or outside a given circle, as well as finding x and y intercepts. Enhance your understanding of circles with practical exercises and solutions.

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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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