Question

Two radio signals are broadcast. The radio waves can be illustrated as a hyperbola with a center at (0,0) a focus of (75,0) and a vertex of (56,0) find equation that describes the radio waves

Answer 1

The equation that describes the radio waves is (x² / 5625) - (y² / 3136) = 1

The standard equation of a hyperbola with a center at (h, k) is :

(x - h)²2 / a² - (y - k)^² / b² = 1

where a= s the distance between the center and the focus,

b = the distance between the center and the vertex.

from the question, we see that the center is at (0, 0), the focus is at (75, 0), and the vertex is at (56, 0).

a = 75 - 0 = 75

b = 56 - 0 = 56

Substituting these values into the standard equation, we get:

(x - 0)² / 75² - (y - 0)² / 56²2 = 1

(x² / 5625) - (y² / 3136) = 1 which is the equation that describes the radio waves