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2.04 The Circle College Algebra: One Step at a Time, Page 234 - 241: #18, 19, 26, 28, 30, 39, 43 Dr. Robert J. Rapalje Seminole State College of Florida Sanford, FL 32773
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
When you
complete the square, remember that you take half of the coefficient, and
square. Half of
This is a
circle with center at
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
Circle
with center at
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
This is a
circle with center at
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
Circle
with center at
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
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
This is a circle with center at
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
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 Half of
This is a circle with center at
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
Circle with center at
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
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
This is
a circle with center at
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
Circle
with center at
p. 240. # 39.
Find the
equation of a circle with center at
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.
Now, the distance between the two points given in this problem, and therefore the radius of the circle, is
Radius =
Radius =
Radius =
Radius =
Therefore the equation of the
circle with center at As a check
(no extra charge!!), you might want to sketch the graph, and see if it does
indeed pass through the point
Final
Answer:
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