$\"\"$

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The polar equation is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Compare the polar equation with standard form $\"\"$ .

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

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The eccentricity of the conic equation is $\"\"$ .

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As eccentricity $\"\"$ , the given conic section is a hyperbola.

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$\"\"$

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The hyperbola equation is $\"\"$ .

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Directrix is perpendicular to the polar axis $\"\"$ .

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Directrix is perpendicular to the polar axis at a distance $\"image\"$ units to the left of the pole.

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The value in the numerator is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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Then the directrix is perpendicular to the polar axis at a distance $\"\"$ units to the left of the pole.

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The directrix is $\"\"$ .

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$\"\"$

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Construct a table for different values of $\"\"$ . \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
$\"\"$ $\"\"$ $\"\"$ $\"\"$ $\"\"$
$\"\"$ $\"\"$ $\"\"$ $\"\"$ \
$\"\"$
\
\

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Graph:

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(1) Graph the polar co-ordinates.

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(2) Plot the points.

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(3) Connect the points to a smooth curve.

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$\"\"$

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$\"\"$

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The eccentricity of the conic equation is $\"\"$ .

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The given conic section is a hyperbola.

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

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The vertices are $\"\"$ and $\"\"$ .

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$\"\"$ .