1. Did you know that the position of your mobile phone can be traced to within 100 metres? Map reproduced from Ordnance Survey map data by permission of the Ordnance Survey © Crown copyright 2010 Mobile Phone Tracking Even if you are not making a call!

2. How it works Base Station Mobile Phone

3. How it works When your phone is on, it regularly sends out a ‘check’ signal which is picked up by nearby base stations. You may have heard this as interference on your car radio, e.g. “di de di di de di..”

4. How it works By comparing the signal strengths and time lags for the signals at each base station, the network can calculate how far your phone is from each base station. r3r3 r2r2 r1r1

5. How it works The location of each base station is defined relative to a suitable set of axes. r3r3 r2r2 r1r1 For example … (–1,2) (4,–1) (5,3)

6. (4,–1) (–1,2) r3r3 r2r2 r1r1 How it works From the calculated distance, the base stations can create imaginary circles on the circumferences of which your phone must lie.

7. (5,3) (4,–1) (–1,2) r3r3 r2r2 r1r1 How it works The 3 circles have one unique point of intersection – the location of the mobile phone.

8. On the 29 th July 2005 one of the suspects from the failed London suicide bombings was tracked to a flat in Rome using this method. http://news.bbc.co.uk/1/hi/technology/4738219.stm Fact

9. (5,3) (4,–1) (–1,2) Can you find the phone? Using the information above, calculate the exact location of the mobile phone. r 1 = 2  5 r 2 =  5 r 3 =  26 Hint Solution

10. Determine the equation of each circle Hint 1

11. (5,3) (4,–1) (–1,2) Can you find the phone? Using the information above, calculate the exact location of the mobile phone. r 1 = 2  5 r 2 =  5 r 3 =  26 Hint Solution

12. Express the circle equations in the form: x 2 + y 2 + 2gx + 2fy + c = 0 Take two circles and solve simultaneously by the elimination method to obtain a linear equation Hint 2

13. (5,3) (4,–1) (–1,2) Can you find the phone? Using the information above, calculate the exact location of the mobile phone. r 1 = 2  5 r 2 =  5 r 3 =  26 Hint Solution

14. Solve the linear equations to find the point of intersection of the three circles Hint 3

15. (5,3) (4,–1) (–1,2) Can you find the phone? Using the information above, calculate the exact location of the mobile phone. r 1 = 2  5 r 2 =  5 r 3 =  26 Solution

16. (3,4) Were you right? Solution