Warm-Up Find the values of x and y..

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Presentation transcript:

Warm-Up Find the values of x and y.

Homework Answers 1) 110° 2) 220° 3) 90° 4)x = 7 5) x = 5 6) P = 59.6 7) 236° 8) 30976𝜋 225 𝑐 𝑚 2 or 432.5 𝑐 𝑚 2 9) 149𝜋 15 𝑚 or 31.2 m 10) 2160 17𝜋 𝑐𝑚 or 40.4 cm 11) 5.9 cm

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.

Equation of a Circle in Standard Form Vocabulary! Equation of a Circle in Standard Form

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

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. x2 + (y – 3)2 = 18

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

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 line.

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

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.

Warm-Up Write the equation of the circle. Write the equation of a circle that has its center at (-3, 3) and passes through (-6, 2).

Homework Answers

Example 6: c) Jimmy Johns offers delivery within 5 miles of the restaurant. Marcus’ house is located 4 miles east and 5 miles south of Jimmy Johns. Carly’s house is located 1 mile west and 2 miles south of Jimmy Johns. Conner’s house is located 3 miles east and 5 miles north of Jimmy Johns. If Jimmy Johns is located at (–2, 1), which house(s) can get delivery?

Example 6: d) Cell phone towers are periodically placed around App Town so that they give a signal that reaches within 4 miles of the tower’s location. One particular tower is located at (3, 4). Houses A, B, and C are located at (–1, 4), (5, 3), and (2, 0). Which house(s) receive a signal from this tower?

Summary!