1. The document discusses problems involving the equation of a circle. It provides examples of converting general circle equations to standard form and determining the equation of a circle given properties like the center and radius or a point it contains. 2. It also gives an example of finding the equation of a circle when given the diameter and center, or when a line passes through the center and intersects the circle at two points. 3. Finally, it provides a word problem about cellular phone towers with different radii and transmission boundaries, and asks to determine the tower servicing given points and which network would be best to subscribe to.

1. PROBLEMS INVOLVING EQUATION OF A CIRCLE
Review: Convert the following general equation to standard form.
1. 𝑥2
+ 𝑦2
+ 2𝑥 − 6𝑦 + 7 = 0
2. 𝑥2
+ 𝑦2
− 2𝑥 − 4𝑦 + 1 = 0

2. 1. Find the general equation of a circle
whose center is (2,6) and whose radius
is 3.

3. 2. Determine the general equation of
the circle whose center is (3,-1) and
whose graph contains the point (7,-1).

4. 3. Determine the general equation of
the circle whose center is (-3,5) and
whose graph contains the point (-2,1).

5. 3. The diameter of a circle is 18 units
and its center is at (-3,8).What is the
equation of the circle?

6. 4. A line passes through the center of a
circle and intersects it at points (2,3)
and (8,7). What is the equation of the
circle?

7. 5. Cellular phone networks use towers to transmit calls to a circular
area. On a grid of a province, the coordinates that correspond to the
location of the towers and the radius each covers are as follows: Wise
Tower is (-5,-3) and covers a 9 km radius; Global Tower is at (3,6) and
covers a 4 km radius; and Star Tower is at (12,-3) and covers a 6 km
radius.
A. What equation represents the transmission boundaries of each tower?
B. Which tower transmits calls to phones located at (12,2)?(-6,7)?(2,8)?(1,3)?
C. If you were a cellular phone user, which cellular phone network will you
subscribe to? Why?