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 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

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

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

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

Ex. 1: Writing a Standard Equation of a Circle centered at (0, 0) and radius 7.1 x 2 + y 2 = r 2 Standard equation of a circle. x 2 + y 2 = = Simplify.

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.

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)

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

Find the x and y intercepts algebraically.