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### Algebra

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- x
^{2}- 4y^{2}+4x+32y-96=0 - The asymptotes of a hyperbol are given by the equation 4x - y = -16 and 4x + y = -8. Find the equation of the hyperbola if one of the foci is located at (-3 - √17, 4).
- Find the standard form of the equation of the hyperbola with the given characteristics.

vertices: (0, ±4) foci: (0, ±5) - 4. Two radio transmitters positioned 400 miles apart along the shore send simultaneous signals to a ship that is 250 miles offshore, sailing parallel to the shoreline. The signal from transmitter A reaches the ship 300 microseconds before the signal from transmitter B. The signals travel at a speed of 186,000 miles per second, or 0.186 mile per microsecond. Find the equation of the hyperbola with foci A and B on which the ship is located