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The Standard Form of the Equation of a Circle
(
h
,
k
) is the center
r
is the radius
(
x
,
y
) is any point on the circle
All points (
x
,
y
) on the circle are a fixed distance (radius) away from the center (
h
,
k
).
The
h
value of your center is the first value of your ordered pair and the
k
value of your
center is the second value of your ordered pair.
We can use this form to plug into when we need to come up with the equation of a
circle.
When writing an equation of a circle, keep in mind that
you ALWAYS need two
pieces of information:
1.
The center of the circle.
2.
The radius of the circle.
Once you have these two pieces of information, you plug the
h
and
k
values from
your center and the value of the radius (
r
) into the standard form of the equation
of a circle.
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View Full Document Example 1:
Write the standard form of the equation of the circle with
center (5, 7) and
r
= 4.
What are the two things we need to write an equation of a circle????
If you said
the center and the radius,
you are correct.
Looks like we have all the information we need. We are ready to put our equation together.
What value are we going to replace
h
with?
If you said 5, you are correct!!!
h
is the first number of the ordered pair of the center of the
circle.
What value are we going to replace
k
with?
If you said 7, you are right on!!!
k
is the second number of the ordered pair of the center of the
circle.
What value are we going to replace
r
with?
If you said 4, give yourself a pat on the back!!!
r
is the radius of the circle.
Putting it into standard form we get:
*Plug in 5 for
h
, 7 for
k
, and 4 for
r
*4 squared is 16
*Standard form of circle with center (5, 7) and
radius 4
Example 2:
Write the standard form of the equation of the circle with
.
What are the two things we need to write an equation of a circle????
If you said
the center and the radius,
you are correct.
Looks like we have all the information we need. We are ready to put our equation together.
What value are we going to replace
h
with?
If you said 3, you are correct!!!
h
is the first number of the ordered pair of the center of the
circle.
What value are we going to replace
k
with?
If you said 1, you are right on!!!
k
is the second number of the ordered pair of the center of the
circle.
What value are we going to replace
r
with?
If you said square root of 10, give yourself a pat on the back!!!
r
is the radius of the circle.
Putting it into standard form we get:
*Plug in 3 for
h
, 1 for
k
, and sq. root
of 10 for
r
*sq. root of 10 squared is 10
*Standard form of circle with center (
3,1) and radius of sq. root of 10
Make sure that you are careful when one of your values is negative and
you have to subtract it as we did in line 2.
x
 (3) is not the same as
x
 3
and
y
 (1) is not the same as
y
 1.
Example 3:
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This note was uploaded on 02/18/2011 for the course MATH 101 taught by Professor Kindle during the Spring '11 term at South Texas College.
 Spring '11
 Kindle
 Algebra

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