$\"\"$

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The equation of the curves are $\"\"$ and $\"\"$ .

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Find the point of intersection of the curves by equating both the curves.

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$\"\"$ .

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The point of intersections of the curves are $\"\"$ and $\"\"$ .

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$\"\"$

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Consider the point is $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Slope of the tangent line is the derivative of the function at a particular point.

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Slope of the tangent line at $\"\"$ .

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$\"\"$ .

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Slope of the tangent line to the curve $\"\"$ is $\"\"$ .

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$\"\"$

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Consider the point is $\"\"$ .

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Slope of the tangent line is the derivative of the function at a particular point.

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Slope of the tangent line at $\"\"$ .

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$\"\"$ .

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Slope of the tangent line to the curve $\"\"$ is $\"\"$ .

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$\"\"$

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Two lines are said to be perpendicular if product of the their slope is equal to $\"\"$ .

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Slope of the tangent line to the curve $\"\"$ is $\"\"$ .

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Slope of the tangent line to the curve $\"\"$ is $\"\"$ .

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$\"\"$

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Product of the slopes of the tangent lines is equal to $\"\"$ .

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The tangent lines of the two curves are perpendicular at their points $\"\"$ and $\"\"$ .

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$\"\"$

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The tangent lines of the two curves are perpendicular at their point $\"\"$ and $\"\"$ .