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9.3 – Circles with Coordinates and Proofs
Key Terms
 Circle – All points on a plane that are the same distance from a single point.
 Center of the Circle – The point exactly in the middle of a circle.
 Origin – Where x and y coordinates are both zero on a coordinate plane.
 Radius – The distance from the center of a circle to any point on the circle.
 The size of a circle is defined by its radius.
Review
Solutions for Lines and Circles 
 The solution set for the equation of a line is all the points that lie on the line.
 The solution set for the equation of a circle is all the points that lie on the circle.

 Circle Formula and Coordinates


Notes
Distance Formula: Used to Find the Radius of a Circle 

Standard Equation for Circle Centered at Origin 
Standard Equation for Any Circle 

 r = radius of the circle
 x = xcoordinate of point on the circle
 y = ycoordinate of point on the circle
 Ex. Circle centered at the origin with radius 8


 r = radius of the circle
 (x, y) = a point on the circle
 (h, v) = center of the circle
 h: horizontal (xcoordinate)
 v: vertical (ycoordinate)
 Ex. Circle centered at (3,5) with radius 5

Moving the Circle 
Graphing and Writing the Equation of a Circle 
 When you move the circle left or right, the number that changes in its equation is the xcoordinate of the center.
 When you move the circle up or down, the number that changes in its equation is the ycoordinate of the center.

 To write the equation for any circle, you need to know its radius and the coordinates of its center.
 You can use the equation of a circle to graph the circle on an xyplane and find the coordinates of points on the circle.

Quadrants 
Circles on the Axes 
 Each xyplane has 4 quadrants
 Quadrant I
 Top right: (+,+)
 Quadrant II
 Top left: (,+)
 Quadrant III
 Bottom left: (,)
 Quadrant IV
 Bottom right: (+,)

 Circles Centered on the xaxis
 Circles Centered on the yaxis
 Ex. The following circles have their centers in the second quadrant.
 Ex. The following circles have their centers in the third quadrant.

Examples
Important!
Practice (Apex Study 9.3)
 Try practice problems on Pgs 10, 22
 Mandatory: write and answer problems on Pgs 11, 23
 2 Quizzes
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