Loran is a long range hyperbolic navigation system. suppose two loran transmitters are located at the coordinates (-100,0) and (100,0), where unit distance on the coordinate plane is measured in miles. a receiver is located somewhere in the first quadrant. the receiver computes that the difference in the distances from the receiver to these transmitters is 180miles. what is the standard form of the hyperbola that the receiver sits on if the transmitters behave as a foci of the hyperbola

Step-by-step explanation:

center of the hyperbola  is  (0,0)  = (h, k)

c = the distance form the center to either focal point  = 100

The differences  from the receiver to the transmitters  =  2a

2a =  180  miles

a   =  180/2=90 miles

The standard form is

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it