Section 10 8 Equation of Circle Learning Targets

Section 10. 8: Equation of Circle Learning Targets Students will be able to write the equation of a circle. Students will be able to graph a circle on the coordinate plane.

Vocabulary! Equation of a Circle in Standard Form Center: Radius:

Example 2: Find the center and radius of each equation. a. (x + 3)2 + (y – 1)2 = 4

Example 2: Find the center and radius of each equation. b. x 2 + (y – 3)2 = 18

Example 2: Find the center and radius of each equation. c. (y + 8)2 + (x + 2)2 = 72

Example 1: Graph the following circle: a. (x - 3)2 + (y + 1)2 = 4

Example 1: Graph the following circle: b. (x – 2)2 + (y – 5)2 = 9

Example 1: Graph the following circle: c. (y + 4)2 + (x + 2)2 = 16

Brain Break! 1. Stand Up. 2. Take a pen and flip it ONE REVOLUTION. (Imagine a piece of tape on one end of the pen, then throw the pen from the tape side. Have the pen go one full turn around to get to the tape side again) 3. Now do the same thing with your other hand. 4. Now get a pen for both hands and try to do both pens at the same time. 5. If you really are good at that, then try to throw the pens up into the air and catch them in opposite hands. This is tough.

Example 3: a) Write the equation of the circle with a center at (3, – 3) and a radius of 6.

Example 3: b) Write the equation of the circle graphed below.

Example 3: c) Write the equation of the circle graphed below.

You Try! Example 4: Write the equation of the circle.

You Try! Example 4: Write the equation of the circle.

Example 5: a) Write the equation of the circle that has its center at (– 3, – 2) and passes through (1, – 2).

Example 5: b) Write the equation of the circle that has its center at (– 1, 0) and passes through (3, 0).

Example 6: a) ELECTRICITY Strategically located substations are extremely important in the transmission and distribution of a power company’s electric supply. Suppose three substations are modeled by the points D(3, 6), E(– 1, 1), and F(3, – 4). Determine the location of a town equidistant from all three substations, and write an equation for the circle.

Example 6: b) AMUSEMENT PARKS The designer of an amusement park wants to place a food court equidistant from the roller coaster located at (4, 1), the Ferris wheel located at (0, 1), and the boat ride located at (4, – 3). Determine the location for the food court.

Summary!

Day 1 Homework: Pg. 760, #14, 15, 18, 19, 23 & Ch. 10 Rev. WS - #1 – 37 odd