10-3 Circles

Objectives To write and graph the equation of a circle

To find the center and radius of a circle and use them to graph the circle

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A circle is the set of all points in a plane that are a distance r from a given point, the center of a circle. The distance r is the radius of the circle. The use of distance in these definitions makes the distance formula d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d equals . square root of open . x sub 2 , minus , x sub 1 . close squared . plus . open . y sub 2 , minus , y sub 1 . close squared end root  a useful tool for describing a circle in the coordinate plane.

Essential Understanding An equation of a circle with center (0, 0) and radius r in the coordinate plane is x 2 + y 2 x squared , plus , y squared  = r 2 . r squared , .

Not every circle has its center at the origin. Suppose a circle with radius r has center (h, k). Then r is the distance from (h, k) to any point (x, y) on the circle.

r = ( x − h ) 2 + ( y − k ) 2 Distance formula r 2 = ( x − h ) 2 + ( y − k ) 2 Square each side. table with 2 rows and 3 columns , row1 column 1 , r , column 2 equals . square root of open , x minus h , close squared . plus . open , y minus k , close squared end root , column 3 cap distanceformula , row2 column 1 , r squared , column 2 equals . open x minus h close squared . plus . open y minus k close squared , column 3 cap squareeachside. , end table

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