$\"\"$

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Observe the graph :

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Since the $\"\"$ -coordinates of foci are same, the hyperbola has a horizontal transverse axis.

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The standard form of hyperbola with horizontal transverse axis is $\"\"$ .

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Where,

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$\"\"$ ,

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Center : $\"\"$ ,

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Vertices : $\"\"$ ,

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Foci : $\"\"$ ,

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Transverse axis : $\"\"$ ,

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Conjugate axis : $\"\"$ ,

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Eccentricity : $\"\"$ .

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Asymptotes : $\"\"$ . $\"\"$

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

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The distance from a focus to the center is $\"\"$ units.

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So, $\"\"$ .

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From the given information $\"\"$ .

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Find the value of $\"\"$ by using the values of $\"\"$ and $\"\"$ .

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$\"\"$

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Substitute the values $\"\"$ and $\"\"$ in standard form of hyperbola.

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$\"\"$

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$\"\"$ .

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$\"\"$

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The equation for the equilateral hyperbola is $\"\"$ .