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The tangent line equation $\"\"$ is tangent to a circle at $\"\"$ .

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The tangent line equation $\"\"$ is tangent to a circle at $\"\"$ .

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If a line is tangent to a circle, then the line perpendicular to the tangent line passing through the point of tangency also passes through the center of the circle.

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Find the perpendicular lines of tangent lines.

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These lines passes through the center of the circle.

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Consider the equation $\"\"$ .

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Write the equation in slope-intercept form $\"\"$ , where $\"\"$ is slope and $\"\"$ is $\"\"$ -intercept.

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$\"\"$ .

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Slope of the line is $\"\"$ .

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Perpendicular line slope is $\"\"$ .

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Perpendicular line passes through $\"\"$ .

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

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$\"\"$

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$\"\"$ .

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Another tangent equation $\"\"$ .

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Compare with $\"\"$ .

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Slope of the line is $\"\"$ .

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Perpendicular line slope is $\"\"$ .

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Perpendicular line passes through $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Find the intersection points of $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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

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$\"\"$

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The intersection point is $\"\"$ .

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Center of the circle is $\"\"$ .

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Center of the circle is $\"\"$ .