GEOMETRYHELP

[x – (–8)]2 + (y – 0)2 = ( 5 )2 Substitute (–8, 0) for (h, k) and 5 for r.

Write the standard equation of a circle with center

(–8, 0) and radius 5.

(x – h)2 + (y – k)2 = r2 Standard form

(x + 8)2 + y2 = 5 Simplify.

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Circles in the Coordinate PlaneLESSON 12-5

Additional Examples

GEOMETRYHELP

r = (x – h)2 + (y – k)2 Use the Distance Formula to find r.

= (–15 – 5)2 + (–13 – 8)2 Substitute (5, 8) for (h, k) and (–15, –13) for (x, y).

Write the standard equation of a circle with center (5, 8) that

passes through the point (–15, –13).

First find the radius.

= (–20)2 + (–21)2 Simplify.

= 400 + 441

= 841 = 29

Circles in the Coordinate PlaneLESSON 12-5

Additional Examples

GEOMETRYHELP

Then find the standard equation of the circle with center (5, 8) and radius 29.

(continued)

(x – h)2 + (y – k)2 = r2 Standard form

(x – 5)2 + (y – 8)2 = 292 Substitute (5, 8) for (h, k) and 29 for r.

(x – 5)2 + (y – 8)2 = 841 Simplify.

Circles in the Coordinate PlaneLESSON 12-5

Additional Examples

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GEOMETRYHELP

Find the center and radius of the circle with equation

(x + 4)2 + (y – 1)2 = 25. Then graph the circle.

(x + 4)2 + (y – 1)2 = 25(x – (– 4))2 + (y – 1)2 = 52 Relate the equation to the standard form

(x – h)2 + (y – k)2 = r2. h k r

The center is (– 4, 1) and the radius is 5.

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Circles in the Coordinate PlaneLESSON 12-5

Additional Examples

GEOMETRYHELP

A diagram locates a radio tower at (6, –12) on a coordinate

grid where each unit represents 1 mi. The radio signal’s range is 80 mi.

Find an equation that describes the position and range of the tower.

The center of a circular range is at (6, –12), and the radius is 80.

(x – h)2 + (y – k)2 = r2 Use standard form.

(x – 6)2 + [y – (–12)]2 = 802 Substitute.

(x – 6)2 + (y + 12)2 = 6400 This is an equation for the tower.

Circles in the Coordinate PlaneLESSON 12-5

Additional Examples

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