Find the equation of the hyperbola.
Two microphones, I mile apart, record an explosion. Microphone A receives the sound 2 seconds beforemicrophone B. Find the equation of the hyperbola that represents the position of where the explosion occurred (Use 1 mile = 5280 feet and that sound travels at 1100feet per second).
(2 seconds x (1100 ft/sec) x (1 mile/5280 ft)) = 5/12 miles
2a = (5/12)
a = 5/24
Using the equation (y^2)/(a^2) - (x^2)/(b^2) I determined:
(y^2)/((5/12)^2) - (x^2)/(b^2)
I'm not sure what to do beyond this point and I'm not even sure if I've taken the right steps. Let me know if anything needs clarification.
Re: Find the equation of the hyperbola.
The equation for the hyperbola is y^2/a^2 - x^2/b^2 = 1. You have a = 5/24 (although you miswrote it as 5/12 in the last line of your post), so now you need to find the value of 'b'. Use the formula c^2 = a^2 + b^2, where for a hyperbola 'c' = the distance from the center to each focus, which for this problem is 1/2 mile. Can you finish it from here?