p.
237 # 18. 
Solution: Before you ever start the
problem, you know that this looks like a CIRCLE! The best way to find the
center and radius is by completing the square.
Since you already have coefficients of
and
,
you should begin by re-writing the equation with the x terms together and y
terms together, leaving a space to complete the square:
When you
complete the square, remember that you take half of the coefficient, and
square. Half of 
is
and
is
.
Half of 
is
,
and 
is
.
This is a
circle with center at 
and
with radius 
.
To graph this circle, start at the origin and count 4 units to the left,
then up 3 units. This is the center of the circle. Now, the radius is so
measure 8
units in each direction from the center. The graph should look like this.
Circle
with center at
and
with radius
.
p.
238. # 19 
Solution:
As in #18, this is a
completing the square
problem. Begin by re-writing the equation with the x
terms together and y terms together, leaving a space to complete the
square. Also, you should add +48
to each side of the equation:
When you
complete the square, remember that you take half of the coefficient, and
square. Half of 
is
and
is
.
Half of 
is
,
and 
is
.
This is a
circle with center at 
and
with radius 
.
To graph this circle, start at the origin and count 6 units to the right,
then down 4 units. This is the center of the circle. Now, the radius is
so
measure 10
units in each direction from the center. The graph should look like this.
Circle
with center at and
with radius .
p. 238. # 26.
Solution:
Before you ever start the problem, you know that this looks like a CIRCLE!
The most effective way to find the center and radius is by completing the
square. However, before you can complete the square, you need to have
coefficients of and
.
The best way to accomplish this is to divide both sides of the equation by
.
Rearrange the terms
with the x terms together, and the y terms together, and leave
spaces to complete the square for each variable.
When you complete the square, remember that you take half of the
coefficient, and square. Half of
is
and
is
.
Half of 
is
,
and 
is
.
This is a circle with center at
and
with radius 
.
Page 238. # 28.
Solution:
Before you
ever start the problem, you know that this looks like a CIRCLE! The most
effective way to find the center and radius is by
completing the square. However,
before you can complete the square, you need to have coefficients of
and . The best way to accomplish this is to divide both sides
of the equation by 
.
Rearrange
the terms with the x terms together, and the y
terms together, and leave spaces to complete the square for each variable.
When you
complete the square, remember that you take half of the coefficient, and
square. Half of 
is 
and 
is 
.
Half of is , and 
is 
.
This is a circle with center at
and with radius
.
To graph this circle, start at the origin and count
2.5 units to
the right, then up 1.5
units. This is the center of the circle. Now, the radius is or
1.5
so measure
1.5 units in each
direction from the center. The graph should look like this.
Circle with center at
and of radius
.
p.
239. # 30.
Solution: Before you ever start the problem, you know that this looks like
a CIRCLE! The most effective way to find the center and radius is by
completing the square.
However, before you can complete the square, you need to have coefficients
of and
.
The best way to accomplish this is to divide both sides of the equation by
.
Rearrange the terms with the x terms together, and the y terms
together, and leave spaces to complete the square for each variable.
When you
complete the square, remember that you take half of the coefficient, and
square. Half of is
and
is
.
Half of 
is
,
and 
is
.
This is
a circle with center at 
and
with radius 
,
so 
To graph this circle, start at the origin and
count 2.5 units to the right, then down 0.5 units. This is the center of
the circle. Now, the radius is
or
0.7
so measure about
.7 units(less than 1
unit) in each direction from the center. The graph should look like this.
Circle
with center at and
with radius .
p. 240. # 39.
Find the
equation of a circle with center at
and passing through
.
Solution: In order to find the
equation of a circle, you must know the
center and the
radius of the circle. In this case, you are given the
center, but not the radius of the circle. However, if you know the center
and a point that is ON the circle, then the distance between these two
points is the radius. You must find the distance between the two given
points by the distance formula.
