11-7 Circles in the Coordinate Plane
Holt Geometry
11-7 Circles in the Coordinate Plane
Holt Geometry
11-7 Circles in the Coordinate Plane
Objectives
Write equations and graph circles
in the coordinate plane.
Use the equation and graph of a
circle to solve problems.
Holt Geometry
11-7 Circles in the Coordinate Plane
The equation of a circle is based on the Distance
Formula and the fact that all points on a circle are
equidistant from the center.
Holt Geometry
11-7 Circles in the Coordinate Plane
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 1A: Writing the Equation of a Circle
Write the equation of each circle.
J with center J (2, 2) and radius 4
(x – h)2 + (y – k)2 = r2
Equation of a circle
(x – 2)2 + (y – 2)2 = 42
Substitute 2 for h, 2 for k, and
4 for r.
Simplify.
(x – 2)2 + (y – 2)2 = 16
Holt Geometry
11-7 Circles in the Coordinate Plane
Practice 1: Writing the Equation of a Circle
Write the equation of each circle.
L with center J (-5, -6) and radius 9
(x – h)2 + (y – k)2 = r2
Equation of a circle
(x – (-5))2 + (y – (-6))2 = 92 Substitute -5 for h, -6 for k,
and 9 for r.
Simplify.
(x + 5)2 + (y + 6)2 = 81
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 2: Identifying the center and radius from the
equation of a circle
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 3: Identifying the center and radius from the
graph of a circle
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 4: Writing the equation of a circle given the
center and a point on the circle
P with center P(0, -3) and passes through point (6, 5).
Step 1: Calculate 𝒓𝒂𝒅𝒊𝒖𝒔𝟐
center = (0, -3)
point = (6, 5)
6, 8
∆𝒙, ∆𝒚
(x – h)2 + (y – k)2 = r2
2
2
∆𝑥 + ∆𝑦 = 𝑟
6 2 + 8 2 = 𝑟2
100 = 𝑟 2
Step 2: Plug in center and radius into formula.
(x – h)2 + (y – k)2 = r2
x2 + (y + 3)2 = 100
Holt Geometry
2
11-7 Circles in the Coordinate Plane
Example 5: Writing the equation of a circle given two endpoints.
Writing the equation of  K that passes through endpoints A(5, 4) and B(1, –8).
MP =
5 +1 4 +(−8)
,
2
2
= 3, −2
center = (3, -2)
point = (5, 4)
2, 6
𝟐 2 + 𝟔 2 = 𝑟2
∆𝒙, ∆𝒚
40 = 𝑟 2
(x - 3)2 + (y + 2)2 = 40
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 5: Writing the equation of a circle given two endpoints.
(x – 2)2 + (y - 1)2 = 4
Holt Geometry
11-7 Circles in the Coordinate Plane
Example 6: Writing the equation of a circle from general form to
standard form.
𝟐
𝒃 𝟐
𝟒
𝑿:
→
=
𝟐
𝟐
𝟐
𝟐
𝒃
𝒀:
𝟐
→
−𝟔
𝟐
x2 + 4x + y2 – 6y = -12
x2 + 4x + 4 + y2 – 6y + 9 = -12 + 4 + 9
(x + 2)2 +
(y – 3)2
Center = (-2, 3)
radius = 1
Holt Geometry
= 1
𝟒
=𝟗
11-7 Circles in the Coordinate Plane
𝑿:
𝒃 𝟐
𝟐
𝟐
𝒃
𝒀:
𝟐
𝟐
→
𝟔
𝟐
→
−𝟖
𝟐
=𝟗
𝟐
= 𝟏𝟔
x2 + 6x + y2 – 8y = -24
x2 + 6x + 9 + y2 – 8y + 16 = -24 + 9 + 16
(x + 3)2 +
(y – 4)2
Center = (-3, 4)
radius = 1
Holt Geometry
= 1
11-7 Circles in the Coordinate Plane
Example 7: Graphing a Circle
Graph x2 + y2 = 16.
Holt Geometry
11-7 Circles in the Coordinate Plane
Practice: Graphing a Circle
Graph (x + 5)2 + (y - 2)2 = 4.
Holt Geometry
11-7 Circles in the Coordinate Plane
Holt Geometry
11-7 Circles in the Coordinate Plane
Holt Geometry
11-7 Circles in the Coordinate Plane
Holt Geometry