$\"\"$

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Solve the equations algebraically.

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$\"\"$

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$\"\"$

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From equation (1):

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$\"\"$

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From equation (2):

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$\"\"$

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Equate the the left hand side of equations (3) and (4).

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Apply zero product property.

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

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

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$\"\"$

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Substitute the $\"\"$ values in equation (1).

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For $\"\"$ ,

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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For $\"\"$ ,

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Thus, the intersection points are $\"\"$ and $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Compare it to general form $\"\"$ .

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$\"\"$

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Discriminant $\"\"$

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

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Consider $\"\"$ .

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Compare it to general form $\"\"$ .

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$\"\"$

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$\"\"$

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Since $\"\"$ and $\"\"$ have different signs and equal coefficients,

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the equation represents a circle.

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Graph the equations:

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$\"\"$

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Observe the graph:

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The intersection points are $\"\"$ and $\"\"$ .

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$\"\"$

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The intersection points are $\"\"$ and $\"\"$ .