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Answer:
The location of the new cell phone tower is , and the equation of the circle is
.
Step-by-step explanation:
The location of the cell phone tower coincides with the location of a circunference passing through the three cell phone towers. By Analytical Geometry, the equation of the circle is represented by the following general formula:
(1)
Where:
- Independent variable.
- Dependent variable.
,
,
- Circunference constants.
Given the number of variable, we need the location of three distinct points:
Then, we have the following system of linear equations:
(2)
(3)
(4)
The solution of this system is:
,
,
By comparing the general form with the standard form of the equation of the circunference is:
(5)
(6)
(7)
Where:
,
- Coordinates of the center of the circle.
- Radius of the circle.
If we know that ,
and
, then coordinates of the center of the circle and its radius are, respectively:
,
,
The location of the new cell phone tower is , and the equation of the circle is
.
