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Here in this topic, we will cover the equation of circles on a coordinate plane.

1.
10.6 Equations of a

Circle

Standard Equation of a Circle

Definition of a Circle

Circle

Standard Equation of a Circle

Definition of a Circle

2.
Definition of a Circle

A circle is a set of points a given distance

from one point called the center.

The distance from the center is called the

radius

A circle is a set of points a given distance

from one point called the center.

The distance from the center is called the

radius

3.
Standard equation of the circle

If the circle is at the origin

x2+y2=r2 r is the radius

If the circle is not at the origin

2 2

x h y k r 2

The center is at (h, k)

If the circle is at the origin

x2+y2=r2 r is the radius

If the circle is not at the origin

2 2

x h y k r 2

The center is at (h, k)

4.
Standard equation of the circle

If the circle is at the origin

x2+y2=r2 r is the radius

If the circle is not at the origin

2 2

x h y k r 2

Solve for r

2 2

r x h y k

If the circle is at the origin

x2+y2=r2 r is the radius

If the circle is not at the origin

2 2

x h y k r 2

Solve for r

2 2

r x h y k

5.
Write the equation of Circle

Center at ( -5,0) and radius 4.8

2 2

x h y k r 2

h =?

k =?

r = 4.8

Center at ( -5,0) and radius 4.8

2 2

x h y k r 2

h =?

k =?

r = 4.8

6.
Write the equation of Circle

Center at ( -5,0) and radius 4.8

2 2

x h y k r 2

h =-5 2 2 2

k =0

x 5 y 0 4.8

r = 4.8

2

x 5 2

y 23.04

Center at ( -5,0) and radius 4.8

2 2

x h y k r 2

h =-5 2 2 2

k =0

x 5 y 0 4.8

r = 4.8

2

x 5 2

y 23.04

7.
Write the equation of Circle

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

8.
Write the equation of Circle

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

k=-3 2

2 4 1 3 2

r 2

r= 2 2

x=2 2 4 r 2

y=1 4 16 r 20 2

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

k=-3 2

2 4 1 3 2

r 2

r= 2 2

x=2 2 4 r 2

y=1 4 16 r 20 2

9.
Write the equation of Circle

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

k=-3 2 2

r2 = 20

x 4 y 3 20

2 2

x=2 x 4 y 3 20

Center at ( 4, -3) and

a point on the circle (2,1)

2 2

x h y k r 2

k=-3 2 2

r2 = 20

x 4 y 3 20

2 2

x=2 x 4 y 3 20

10.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6)

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6)

11.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) (5 -13)2 + (6 – 6)2 is it <, >, or = 52

( - 8)2 + 02 = 64 = 25

Greater then outside the circle.

Less then Inside the circle.

Equal is on the circle.

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) (5 -13)2 + (6 – 6)2 is it <, >, or = 52

( - 8)2 + 02 = 64 = 25

Greater then outside the circle.

Less then Inside the circle.

Equal is on the circle.

12.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

13.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9)

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9)

14.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

15.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

(16, 2)

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

(16, 2)

16.
Given the equation of the Circle

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

(16, 2) On

(x – 13)2 + (y – 6)2 = 52

Tell if the point is inside or outside the circle.

(5, 6) Outside

(14,8) In

(20, 9) Outside

(16, 2) On

17.
Homework

Page 638 – 639

# 7 – 25 , 33 - 39

Page 638 – 639

# 7 – 25 , 33 - 39