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Math 2 Precalculus Algebra

Name________________________

Date_________________________

Circles — 2.4

(

)

(

)

(

)

=

−

2

+

−

2

d

x

x

y

y

1.

Use the distance formula

to write an equation of all of the coordinates

, x y

2

1

2

1

(

)

that are a distance, r, from the point

, h k and then illustrate this concept graphically.

Standard Form of the Equation of a Circle

The graph of circle is given by the equation:

(

)

(

)

−

2

+

−

2

=

2

x h

y k

r

,

(

)

where is the

, h k center of the circle and r is the radius of the circle.

Note:

(

)

+

=

2

2

2

x

y

r

If the center of the circle is

0 , 0 then the equation becomes

.

(

)

+

=

2

2

x

y

1

If the center of the circle is

0 , 0 and the radius is 1, then the equation becomes

. This circle is called the

unit circle.

General Form of the Equation of a Circle

The graph of circle may also be written by the equation:

+

+

+

+

=

2

2

x

y

ax

by

c

0

(

)

Write the standard form of the equation and the general form of the equation of the circle of radius r and center

, h k .

Graph the circle.

(

)

(

)

h k =

r =

2.

4

;

,

0 , 2

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Parent category: Education