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$\"\"$

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The conic equation is $\"\"$ .

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The general form of the conic equation is $\"\"$ .

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Identify the conic section using the discriminant of $\"\"$ .

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If a circle $\"\"$ ; $\"\"$ and $\"\"$ .

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If an ellipse $\"\"$ ; either $\"\"$ and $\"\"$ .

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If a hyperbola $\"\"$ .

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If an parabola $\"\"$ .

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$\"\"$

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The conic equation is $\"\"$ .

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Rewrite the equation as $\"\"$ .

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Compare $\"\"$ with the general equation $\"image\"$ .

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Here $\"\"$ .

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

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$\"\"$ .

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The discriminant is $\"\"$ , hence the conic is hyperbola.

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

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The hyperbola equation is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The standard form of hyperbola is $\"\"$ .

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Compare $\"\"$ with standard form.

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Here $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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The foci is $\"\"$ .

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$\"\"$ .

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

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$\"\"$

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

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Vertices $\"\"$ and $\"\"$ .

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$\"\"$

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(a) The equation represents hyperbola.

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(b) Vertices $\"\"$ and $\"\"$ and foci $\"\"$ .