$\"\"$

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The equation is $\"\"$ , $\"\"$ , $\"\"$ .

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$\"\"$ and $\"\"$ are opposite signs.

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$\"\"$

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$\"\"$

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$\"\"$

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Completing the squares by adding $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Let $\"\"$ .

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$\"\"$ .

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$\"\"$

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(a)

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If $\"\"$ .

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$\"\"$

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$\"\"$

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Here $\"\"$ and $\"\"$ are opposite signs.

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Therefore, the equation $\"\"$ represents a hyperbola.

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$\"\"$

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(b)

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If $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The graph of the above equation represents two intersecting lines through the point $\"\"$ with slope $\"\"$ .

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$\"\"$

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(a) The equation $\"\"$ represents a hyperbola.

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(b) The equation $\"\"$ represents two intersecting lines through the point $\"\"$ with slope $\"\"$ .