Chapter 10 Circles - 10.6 Equations Of Circles Worksheet
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10.6
Equations of Circles
GOAL
1
F
E
C
INDING
QUATIONS OF
IRCLES
What
you should learn
GOAL
Write the equation
1
You can write an equation of a circle in a coordinate plane
y
(x, y )
of a circle.
if you know its radius and the coordinates of its center.
r
Suppose the radius of a circle is
r
and the center is
k).
(h,
Use the equation
GOAL
2
(h, k )
Let (x, y) be any point on the circle. The distance between
of a circle and its graph to
solve problems.
(x, y) and
(h, k)
is r, so you can use the Distance Formula.
x
Why
2
2
you should learn it
h
k
r
(x º
)
+ ( y º
)
=
To solve real-life
Square both sides to find the
standard equation of a circle
with radius r and
problems, such as deter-
center (h, k).
mining cellular phone
2
2
2
coverage, as in
(x º h)
+ (y º k)
r
=
Standard equation of a circle:
Exs. 41 and 42.
2
2
2
If the center is the origin, then the standard equation is x
+ y
= r
.
Writing a Standard Equation of a Circle
E X A M P L E 1
Write the standard equation of the circle with center
and radius 7.1.
(º4, 0)
S
OLUTION
2
2
2
(x º h)
+ (y º k)
=
r
Standard equation of a circle
2
2
2
[x º (º4)]
+ (y º 0)
=
7.1
Substitute.
2
2
(x + 4)
+ y
= 50.41
Simplify.
Writing a Standard Equation of a Circle
E X A M P L E 2
The point (1, 2) is on a circle whose center is (5, º1). Write the standard
equation of the circle.
S
OLUTION
the radius. The radius is the distance from the point (1, 2) to the center (5, º1).
Find
2
2
r = (5 º 1 )
+ ( º 1 º 2 )
Use the Distance Formula.
2
2
r = 4
+ ( º 3 )
Simplify.
r = 5
Simplify.
(h, k) =
and r =
into the standard equation of a circle.
Substitute
(5, º1)
5
2
2
2
(x º 5)
+ (y º (º1))
=
5
Standard equation of a circle
2
2
(x º 5)
+ (y + 1)
= 25
Simplify.
636
Chapter 10 Circles
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