Circles in the Coordinate Plane Geometry 11 5

Circles in the Coordinate Plane Geometry 11 -5

Get your supplies • Graph Paper • Compass? Equation Exploration

1. Make a table of values to graph the equation 2 2 x +y =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 2 2 (x-3) +(y-3) =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 Equation Exploration

• 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) Standard Equation of a Circle

Example

Example

Example

Example

Example

Circles in the Coordinate Plane Sample Problems

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

Practice

Practice

Practice

Practice

Practice

Practice

Practice

Interior On Exterior On Interior

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

• Pages 617 – 619 • 2, 6, 8, 10, 12, 16, 18, 28, 30, 32, 34, 36, 64 Honors Homework