4'4 Equations of Circles

1
4.4 Equations of Circles

• Algebra I/Geometry
• High School

2
Teacher Page

• Content Finding the equation of a circle given
  the center and radius. Finding the center and
  radius of a circle given the equation
• Grade Level Algebra 2
• Creator Don Sutcliffe
• Other Print slides 14-23 as a handout for
  students to take notes.

3
Teacher Page

• Curriculum Objectives
• Algebra 2 VI.C The learner will be able to
  graph, analyze, and write the equations of
  circles.
• MAP Objectives
• Missouri Show-Me Standard Math MA2, MA4, MA5
• Missouri Show-Me Standard Goal G3.4, G3.5

4
Circle

• A set of all points in a plane that are an equal
  distance from a given point, called the center.

C
Named by the center Circle C
or C
5
Diameter

• A segment that passes through the center of a
  circle and whose endpoints lie on the circle.

6
Radius

• A segment whose endpoints are the center and a
  point on the circle.

7
Equation of a circle

• The equation of a circle is derived from the
  distance formula.
• Using point (x,y) that lies on the circle, center
  (h,k), and radius r.

Dv(x2-x1)2(y2-y1)2
(x,y)
rv(x-h)2(y-k)2
r
By squaring both sides we get
(h,k)
r2(x-h)2(y-k)2
8

• Write the equation of a circle with C(2,4) and
  radius 5.

r2(x-h)2(y-k)2
52(x-2)2(y-4)2
25(x-2)2(y-4)2
9

• Write the equation of a circle with C(-3,1) and
  radius 9.

r2(x-h)2(y-k)2
92(x-(-3))2(y-1)2
81(x3)2(y-1)2
10

• Write the equation of a circle with center at the
  origin, (0,0) and radius 6.

r2(x-h)2(y-k)2
62(x-0)2(y-0)2
36x2y2
11

• What is the center and radius of the circle with
  equation 3(x-1)2(y4)2.

r2(x-h)2(y-k)2
C(h,k)
r23
C(1,-4)
rv3
12

• What is the center and radius of the circle with
  equation 16(x2)2(y-3)2.

r2(x-h)2(y-k)2
C(h,k)
r216
C(-2,3)
r4
13
End Show
14
4.4 Equations of Circles

• Algebra I/Geometry
• High School

15
Circle

• A set of all points in a plane that are an equal
  distance from a given point, called the center.

C

16
Diameter

• A segment that passes through the center of a
  circle and whose endpoints lie on the circle.

17
Radius

• A segment whose endpoints are the center and a
  point on the circle.

18
Equation of a circle

• The equation of a circle is derived from the
  distance formula.
• Using point (x,y) that lies on the circle, center
  (h,k), and radius r.

(x,y)
r
By squaring both sides we get
(h,k)
19

• Write the equation of a circle with C(2,4) and
  radius 5.

r2(x-h)2(y-k)2
20

• Write the equation of a circle with C(-3,1) and
  radius 9.

r2(x-h)2(y-k)2
21

• Write the equation of a circle with center at the
  origin, (0,0) and radius 6.

r2(x-h)2(y-k)2
22

• What is the center and radius of the circle with
  equation 3(x-1)2(y4)2.

r2(x-h)2(y-k)2
23

• What is the center and radius of the circle with
  equation 16(x2)2(y-3)2.

r2(x-h)2(y-k)2