Geometry 11-5 Circles in the Coordinate Plane

Equation Exploration Get your supplies Graph Paper Compass?

Equation Exploration 1.Make a table of values to graph the equation x 2 +y 2 =4 2.Complete enough of your table of values to complete the graph

Equation Exploration You should have graphed a complete circle. What is the radius of the circle? Re-write the equation of the circle using the radius instead of a number.

Equation Exploration Make another table of values to graph the equation (x-3) 2 +(y-3) 2 =9 Complete enough of your table of values to complete the graph

Equation Exploration (x-3) 2 +(y-3) 2 =9 What are the coordinates of the center of the circle? (3,3)

Equation Exploration (x-3) 2 +(y-3) 2 =9 What is the radius of the circle? 3

Equation Exploration (x+2) 2 +(y-4) 2 =16 What are the coordinates of the center of the above circle equation? (-2,4)

Equation Exploration What is the radius of a circle defined by the following equation? x 2 +y 2 =49 The radius is 7

Standard Equation of a Circle The standard equation for a circle is written in the following form (x-h) 2 + (y-k) 2 = r 2 The radius of the circle is r The center of the circle is (h,k)

Example

Sample Problems Circles in the Coordinate Plane

Center = (0,4) Radius = 3

Center = (5,0) Radius = 4

Center = (-1,1) Radius = 2

Center = (-4,2) Radius = 5

(x) 2 +(y) 2 =9

(x) 2 +(y-2) 2 =4

(x-1) 2 +(y-1) 2 =1

(x) 2 +(y-1) 2 =4

(x-3) 2 +(y-3) 2 =16

Practice

Interior On Exterior On Interior

Homework Pages 617 – 619 2, 6, 8, 10, 12, 16, 18, 28, 30, 32, 34, 36