Graph and Write Equations of Circles Section 9.3 Graph and Write Equations of Circles

California Standard: 16.0: Students demonstrate and explain how the geometry of the graph of a conic section depends on the coefficients of the quadratic equation representing it.

By following instructions, students will be able to: OBJECTIVE(S): By following instructions, students will be able to: Graph and write equations of circles.

Standard Equation of a Circle with Center at the Origin: The standard form of the equation of a circle with center at (0,0) and radius r is as follows:

EXAMPLE 1: Graph . Identify the radius of the circle.

EXAMPLE 2: The point (2,-5) lies on a circle whose center is the origin. Write the standard form of the equation of the circle.

EXAMPLE 3: What is an equation of the line tangent to the circle at (-3,2)?

U-TRY#1: Graph the equation. Identify the radius of the circle. A) B) C) Write the standard form of the equation of the circle that passes through (5,-1) and whose center is the origin. Write an equation of the line tangent to the circle at (6,1)

Circle and Inequalities: If , then shade inside the circle Circle and Inequalities: If , then shade inside the circle. If , then shade outside the circle.

EXAMPLE 4: A cellular phone tower services a 10 mile radius. You get a flat tire 4 miles east and 9 miles north of the tower. Are you in the tower’s range?

EXAMPLE 5: In example 4, suppose that you fix your tire and then drive south. For how many more miles will you be in range of the tower?

HOMEWORK Sec 9.3 WS