Transcript Circles in the Coordinate Plane LESSON 12-5 Additional Examples Write the standard equation of a circle with center (–8, 0) and radius 5. (x –

Circles in the Coordinate Plane
LESSON 12-5
Additional Examples
Write the standard equation of a circle with center
(–8, 0) and radius 5.
(x – h)2 + (y – k)2 = r2
[x – (–8)]2 + (y – 0)2 = (
(x + 8)2 + y2 = 5
Standard form
5 )2
Substitute (–8, 0) for (h, k) and
5 for r.
Simplify.
Quick Check
HELP
GEOMETRY
Circles in the Coordinate Plane
LESSON 12-5
Additional Examples
Write the standard equation of a circle with center (5, 8) that
passes through the point (–15, –13).
First find the radius.
(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).
=
(–20)2 + (–21)2
Simplify.
=
400 + 441
=
841 = 29
r=
HELP
GEOMETRY
Circles in the Coordinate Plane
LESSON 12-5
Additional Examples
(continued)
Then find the standard equation of the circle with center (5, 8)
and radius 29.
(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.
Quick Check
HELP
GEOMETRY
Circles in the Coordinate Plane
LESSON 12-5
Additional Examples
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
HELP
GEOMETRY
Circles in the Coordinate Plane
LESSON 12-5
Additional Examples
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
(x – 6)2 + [y – (–12)]2 = 802
(x – 6)2 + (y + 12)2 = 6400
Use standard form.
Substitute.
This is an equation for the tower.
Quick Check
HELP
GEOMETRY