An example of hyperbola and its standard equation Examples are: When a shell explodes somewhere, the time of the explosion sound heard at a is 2 s later than that at B. It is known that the distance between AB and ab is 800 m and the sound velocity is 340 m / s. The equation of the explosion point curve is obtained (let the explosion point be p (x, y); establish a rectangular coordinate system so that AB is on the X axis, and point O coincides with the midpoint of line AB) In the process of solving the problem, there is one step "Because pa - Pb = 340 * 2 = 680 > 0, x > 0" I can't figure out why "pa - Pb = 340 * 2 = 680 > 0" can lead to "x > 0", and why to determine whether x is greater than 0?

An example of hyperbola and its standard equation Examples are: When a shell explodes somewhere, the time of the explosion sound heard at a is 2 s later than that at B. It is known that the distance between AB and ab is 800 m and the sound velocity is 340 m / s. The equation of the explosion point curve is obtained (let the explosion point be p (x, y); establish a rectangular coordinate system so that AB is on the X axis, and point O coincides with the midpoint of line AB) In the process of solving the problem, there is one step "Because pa - Pb = 340 * 2 = 680 > 0, x > 0" I can't figure out why "pa - Pb = 340 * 2 = 680 > 0" can lead to "x > 0", and why to determine whether x is greater than 0?

Because the absolute value of hyperbolic equation pa-pb is actually two parts of x greater than 0 and less than 0, X less than 0 is pb-pa