Place the two stations on a coordinate grid so that the origin is the midpoint of the segment between Station 1 and Station 2.

The ship is located   farther from Station 2 than Station 1, and from the picture, the ship is located above the -axis. Thus, the ship is located in the second quadrant.

The two stations are located at the foci of the hyperbola, so .

Recall that the absolute value of the difference of the distances from any point on a hyperbola to the foci is .

Because the ship is farther from Station 2 than Station 1,

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Use these values of and to find .

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The transverse axis is horizontal and the center of the hyperbola is located at the origin, so the equation will be of the form .

Substituting the values of and in .

The equation of the hyperbola is .

(b)

The equation of the hyperbola is .

Center: .

Vertices: and .

Foci: and .

Graph the center, vertices, foci.

The hyperbola equation is .

Solve for .

Make a table of values to sketch the hyperbola.

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Graph :

Draw a coordinate plane.

Plot the points obtained in the table.

Sketch the hyperbola.

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(c)

When the ship is from the -axis, then .

Substitute in .

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Since the ship is in the second quadrant, the coordinates of the ship when it is from the -axis are .

(a) The equation of the hyperbola is .

(b) Graph :

(c) The coordinates of the ship when it is from the -axis are .