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 the equation that describes the radio waves.

Question

Extrinix · Answer

@Mirna744 can we get the photos please? (In order would be the best)

Mirna744 · Answer

(0,0), (75,0), and (56,0)

Mirna744 · Answer

those are the numbers for the photos

surjithayer · Answer

distance between center and foci c=75
distance between center and vertex a=56
$$c^2=a^2+b^2$$
$$75^2=56^2+b^2$$
$$b^2=75^2-56^2=(75-56)(75+56)=19 \times 131=2489$$
$$a^2=56^2=3136$$
center=(0,0)
eq. of radio waves is
$$\frac{ x^2 }{ a^2 }-\frac{ y^2 }{b^2 }=1$$
or
$$\frac{ x^2 }{ 3136 }-\frac{ y^2 }{2489 }=1$$