$\"\"$

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Draw the related diagram:

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$\"\"$

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The equation of the hyperbola with center $\"\"$ is $\"\"$ .

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where $\"\"$ are the foci of the hyperbola.

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The distance between the foci is $\"\"$

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The point $\"\"$ is on the hyperbola and it is $\"\"$ from $\"\"$ .

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Hence the value of the $\"\"$ is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$ .

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The point $\"\"$ is on the hyperbola.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore, the second explosion should be set off $\"\"$ due north of point $\"\"$ .

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$\"\"$

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The second explosion should be set off $\"\"$ due north of point $\"\"$ .