$\"\"$

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The hyperbola vertices at $\"\"$ and $\"\"$ and asymptote line at $\"\"$

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The $\"\"$ - coordinates of the focus and vertex are equal.

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The standard form of the hyperbola has a horizontal transverse axis is $\"\"$ .

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Where, $\"\"$ 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 and $\"\"$ .

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The center is the mid point point of vertices of the hyperbola.

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Center $\"\"$ .

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

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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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Compare the asymptote $\"\"$ with general form.

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$\"\"$ .

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

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$\"\"$ .

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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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Therefore, the equation of the hyperbola is $\"\"$ .

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$\"\"$

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

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

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$\"\"$

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The foci is at $\"\"$ and $\"\"$ .

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Find the points to form a rectangle.

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$\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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Asymptotes are $\"\"$ and $\"\"$ . $\"\"$

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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 $\"\"$ , $\"\"$ and $\"\"$ .

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(5) Draw the asymptotes of the hyperbola.

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$\"\"$

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$\"\"$

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

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Graph of the hyperbola :

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$\"\"$ .