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Suppose that a GPS satellite B is located 300 mi due east of GPS satellite A in the space. A car received the signal from B 1196.8 microseconds (us) before it received the signal from A. If the signal travels at the speed of 900ft/js, find Cartesian equation of the hyperbola on which the car lies. 300ml B VORT 1000D NOT HTAM EMAX AMOR

Answer 1

0 solution :- Given that A and B aoe the foci of the lypeobola. (-150,0) А (150.0) 6-150 AB: 300 O, we can worte A:(-150.0) and 32(150,0). Given The distance between A and B = 30mi. which is the distance between sooi Loet o be the center of the ljypcobola 30. C: Half of the distance betueen the faci C = 300 2 6 = 150 mi 2 2 al 1 Equation of My peoboke is a Ý 62 00, we have to find the values of a ando in ordero to get the Equation of Hypoobola. Foom Hypobola, we have the Equation.

C 22 het the P ( The position of car) is the point on Julypcobola. Given. The cat oeceived the cognal foom B = 1196-8 mixcosecondo before it received the Signal from A. ( Time - 1196.8 micosecondo (Ms)). Coivon hal speed of the signal 85 - 900 [feed Irriccoseconds Copeed: Goo Ft Dug). By using the foomula Distance - Speed * Time. I AP-BP) - 900* 1196-8 feet 1 AP-BP) = 1,077,130 feet ca - 1077120 fec? za 1077120 mile's [' milc - TIBO feet 5280 I feet : 1 miles]. 5280 da = 2041 a=204 102 2 a: 102 miles. Q2: (102)2 2 a = 10.uoud the Equation By using 8 = 150²-(102)² [1:62.0?c?] b 2 = 22500 - JOYOU 12,096 12.19.046 ] 2 2 a yo The Equation la is Hyrcabola 10,404 12096

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