12-5 Circles in the Coordinate Plane

Quick Review

The standard form of an equation of a circle with center (h, k) and radius r is ( x − h ) 2 + ( y − k ) 2 = r 2 . open x minus . h , close squared , plus , open y minus . k , close squared , equals , r squared , .

Example

Write the standard equation of the circle shown.

The center is ( − 1 , 2 ) . open minus , 1 comma 2 close .  The radius is 2.

The equation of the circle is ( x − ( − 1 ) ) 2 + ( y − 2 ) 2 = 2 2 open x minus . open minus . 1 close , close squared . plus , open y minus . 2 , close squared , equals , 2 squared  or ( x + 1 ) 2 + ( y − 2 ) 2 = 4 . open x plus . 1 , close squared , plus , open y minus . 2 , close squared . equals 4 .

Exercises

Write the standard equation of each circle below.

22. 
23. 
24. What is the standard equation of the circle with radius 5 and center ( − 3 , − 4 ) ? open minus , 3 comma negative 4 close question mark
25. What is the standard equation of the circle with center (1, 4) that passes through ( − 2 , 4 ) ? open minus , 2 comma 4 close question mark
26. What are the center and radius of the circle with equation ( x − 7 ) 2 + ( y + 5 ) 2 = 36 ? open x minus . 7 , close squared , plus , open y plus . 5 , close squared . equals 36 , question mark

12-6 Locus: A Set of Points

Quick Review

A locus is a set of points that satisfies a stated condition.

Example

Sketch and describe the locus of points in a plane equidistant from points A and B.

The locus is the perpendicular bisector of A B ¯ . eh b bar , .

Exercises

Describe each locus of points.

27. The set of all points in a plane that are in the interior of an angle and equidistant from the sides of the angle.
28. The set of all points in a plane that are 5 cm from a circle with radius 2 cm.
29. The set of all points in a plane at a distance 8 in. from a given line.
30. The set of all points in space that are a distance 6 in. from A B ¯ . eh b bar , .

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