Step 1:

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The hyperbola center is $\"\"$ , focus is $\"\"$ and vertex is $\"\"$ .

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Observe the points, here $\"\"$ coordinates are equal.

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So, the hyperbola has a vertical transverse axis and its standard form of the equation is

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$\"\"$ .

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Where,

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$\"\"$ is the center.

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$\"\"$ is the distance between center and vertex.

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$\"\"$ is the distance between center and focus.

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$\"\"$ .

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The distance between center and vertex is $\"\"$ .

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The distance between center and focus is $\"\"$ .

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$\"\"$

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Substitute the values of $\"\"$ in standard form of the equation.

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$\"\"$

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Step 2:

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

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

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Find the points to form a rectangle.

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$\"\"$ .

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$\"\"$ .

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The extensions of the diagonals of the rectangle are the asymptotes of the hyperbola

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Asymptotes of the hyperbola are $\"\"$ .

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Substitute the values of $\"\"$ in $\"\"$ .

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$\"\"$

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Asymptotes are $\"\"$ .

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Step 3:

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Graph :

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(1) Draw the coordinate plane.

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(2) Draw the equation of the hyperbola.

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(3) Plot the center, foci and vertices.

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(4) Form a rectangle containing the points $\"\"$ , $\"\"$ .

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(5) Draw the asymptotes of the hyperbola.

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$\"\"$

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Solution :

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

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Graph of the hyperbola :

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$\"\"$