Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Bellwork 1.Get a core book from the cabinet/counter. Instead of ripping out the next chapter, you will keep the book with you. 2.Lines m and n are parallel. Calculate the values of x and y. m n

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Rigor - Write equations and graph circles in the coordinate plane, and use the equation and graph of a circle to solve problems. Relevance – signal coverage, search radius, triangulation

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane The equation of a circle is based on the Pythagorean Theorem and the fact that all points on a circle are equidistant from the center. Turn to core book pg 527 to derive the equation of a circle formula

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 1: Writing the Equation of a Circle Write the equation of  J with center J (2, 2) and radius 4.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 2: Writing the Equation of a Circle Write the equation of  K that passes through J(6, 4) and has center K(1, –8).

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane If you are given the equation of a circle, you can graph the circle by identifying and graphing its center and radius.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 3: Graphing a Circle Graph (x – 3) 2 + (y + 4) 2 = 9.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 4: Graphing a Circle Graph (x + 3) 2 + (y - 2) 2 = 4.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Core book examples Turn to pages 528 and 529 to complete examples 2 and 3

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 5: Geology A seismograph measures ground motion during an earthquake. To find the epicenter of an earthquake, scientists take readings in 3 different locations. Then they draw a circle centered at each location. The radius of each circle is the distance the earthquake is from the seismograph. The intersection of the circles is the epicenter. Use the data to find the epicenter of the New Madrid earthquake.

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 5: Geology

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane Example 6: Meteorology Meteorologists are planning the location f a new weather station to cover 3 cities located at J(4, 4), K(–3, –1), and L(2, –8). To optimize radar coverage, the tower must be equidistant from the 3 cities. a)What are the coordinates where the station should be built? b)If each unit of the coordinate plane represents 8.5mi, what is the diameter of the region covered by the radar?

Holt McDougal Geometry 12-7 Circles in the Coordinate Plane 12 – 7 Assignment Part A: textbook pgs 850 – 851 #2 – 8 evens, 11, 12, 16 – 21 Part B: core book pg536 #1 – 7 Due Thursday 4/7 for periods 1, 3, 5, & 7 Due Tuesday 4/12 for periods 2 & 4