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Question 1190114: This problem is all about Equation on circles.
A cellular phone network uses towers to transmit calls. Each tower transmits to a circular area. On a grid of a town, the coordinates of the towers and the circular areas covered by the towers are shown.
36. Write the equations that represent the transmission boundaries of the towers.
37. Tell which towers, if any, transmit to phones located at J(1, 1), K(4, 2), L(3.5, 4.5), M(2, 2.8), and N(1, 6).
I can’t post the illustration but I do hope opening this link would help
https://www.murrieta.k12.ca.us/cms/lib5/CA01000508/Centricity/Domain/1830/T11.7.pdf
(Located 5th page of the pdf, question numbers 36 and 37)
Answering this question would mean a lot to me, thank you!
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Problem 36
Circle A is located at the center (h,k) = (0,0) which is the origin.
The radius of this circle is r = 3 miles
The boundary equation for circle A is
You'll have similar steps for circles B and C.
You should get these equations as answers
Circle B: 
Circle C: 
Let me know if you need to see those steps or not.
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Problem 37
Plot the points mentioned on the same xy grid that the problem starts with.
Now see if any of those points are inside any of the three circles. - Point J(1,1) is in circle A
- Point K(4,2) is in circle B
- Point L(3.5, 4.5) is in circle B and circle C simultaneously
- Point M(2, 2.8) is in none of the circles
- Point N(1,6) is in circle C
The circle the point is located in will have that corresponding tower handle the call. Someone at point L can choose between towers B and C (which one isn't congested). If you're at point M, unfortunately you won't get a cell signal.
Let's say that we didn't have this graph and we wanted to find an algebraic way to figure out which tower will handle the call.
I'll focus on point J(1,1)
Plug in x = 1 and y = 1 into equation A to get...
x^2 + y^2 = 9
1^2 + 1^2 = 9
2 = 9
Which is false. So (1,1) is not on the boundary for circle A. Since the x^2+y^2 value (2) is smaller than the right hand side (9), this means that x^2+y^2 < 9 is the case and (1,1) is inside circle A.
If you were to check circles B and C, then point J won't work.
Trying circle B
(x-5)^2+(y-3)^2 < 6.25
(1-5)^2+(1-3)^2 < 6.25
20 < 6.25
which is false. Circle C is a similar story.
Similar steps and reasoning will help figure out the towers for the other points as well. Point L will work for towers B and C. Point M doesn't work for any of the towers.
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