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NAROL is a long range hyperbolic navigation system. Suppose two NAROL transmitters are located at the

coordinates (-200, 0) and (200, 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 160 miles.

What is the standard form of the hyperbola that the receiver sits on if the transmitters behave as foci of the

hyperbola?

Answer:



Answer :

NORAL follows a hyperbolic path.

Equation of hyperbola; x²/6400 + y²/33600 = 1

Given,

The coordinates where the two NAROL transmitters are located = (-200, 0) and (200, 0)

The distance from receiver to these transmitters = 160 miles

We have to find the standard form of the hyperbola that the receiver sits on ;

Here,

The transmitters behave as foci of the hyperbola.

The center of hyperbola; (h, k) = (0, 0)

The distance from center to focal point,

c = 200

Square both sides

c² = 40,000

The distance from the receiver to the transmitters  is given as:

2a = 160

Divide both sides by 2

a = 80

Square both sides

a² = 6400

We have:

b² = c² - a²

This gives

b² = 40000 - 6400

b² = 33600

The equation of a hyperbola is:

(x - h)²/a² + (y - k)²/b² = 1

So, we have:

(x - 0)²/6400 + (y - 0)²/33600 = 1

Therefore,

The equation of the hyperbola is:

x²/6400 + y²/33600 = 1

Learn more about hyperbola here;

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