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Think about it…

Think about it….

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Think about it…

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  1. Think about it… • You are standing in the middle of the room.  I asks one student to stand 5 feet away from you.  Then I ask 3 more students to also stand 5 feet away from you.  Can you start to picture what is happening?  If all of your classmates were to stand 5 feet away from you, what geometric shape or path would your classmates be forming? 

  2. Circles and Locus of One Point Geometry Unit 7, Day 1 Ms. Reed

  3. Objective: • To learn and understand the equation of a circle. • To find the locus of one point

  4. What is a circle? • A circle is a set of points equidistant from a central point. • A circle is named using its center point. • Radius=distance from center to edge of circle. • Diameter=2 x radius

  5. Equation of a Circle • The circle with center (0,0) and radius r is the graph of the equation • The circle with center (h,k) and radius r is the graph of the equation

  6. Circle Practice: • What is the equation of a circle whose diameter is 24 and whose center is at the origin? • x2 + y2 = 144 • What is the equation of a circle with the center at (1,-3) and radius of 5? • (x-1)2 + (y+3)2 = 25 • Name the coordinates and radius of the center of this circle: (x+3)2 + (y-5)2 = 16 • (-3,5) radius of 4.

  7. More Circle Practice: • An ambulance company provides services within an 80 mile radius of their headquarters.  If this service area is represented graphically,  with the headquarters located at the coordinates (0,0), what is the equation that represents the service area? • x2 + y2 = 6400

  8. Definition • Locus – The set of all points, lines, or planes that satisfy the given information.

  9. Locus Theorem 1: • The locus of points at a fixed distance, d, from point P is a circle with the given point P as its center and d as its radius.

  10. Example: • When he is not in the house, Fido is tied to a stake in the backyard.  His leash, attached to the stake, is 15 feet long.  When traveling at the end of his leash, what is the locus of Fido's path? • A circle such that the center is the stake with a radius of 15ft

  11. More Practice: • http://www.regentsprep.org/Regents/math/geometry/GL1/PracLoc1.htm

  12. Homework • Work Packet: Circles and Locus of One Point

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