Circles in the Coordinate Plane Geometry 11-5

Get your supplies Graph Paper Compass? Equation Exploration

Make a table of values to graph the equation x2+y2=4 Complete enough of your table of values to complete the graph Equation Exploration

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

(x-3)2+(y-3)2=9 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

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

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

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? x2+y2=49 The radius is 7 Equation Exploration

Standard Equation of a Circle The standard equation for a circle is written in the following form (x-h)2 + (y-k)2 = r2 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 Exterior On Interior

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

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