geometry help [x – (–8)] 2 + (y – 0) 2 = ( 5 ) 2 substitute (–8, 0) for (h, k) and 5 for r....
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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.
Quick Check
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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