$\"\"$

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The equation of the curve is $\"\"$ .

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Find the tangent line to the curve and is perpendicular to $\"\"$ .

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The curve is $\"\"$

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

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$\"\"$ .

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The slope of the curve is $\"\"$ .

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The equation is $\"\"$ .

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$\"\"$

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The slope of the equation is $\"\"$ .

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The tangent line to the curve is perpendicular to the line $\"\"$ .

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Hence, $\"\"$ .

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

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$\"\"$

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$\"\"$

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Take natueal logarithm on each side

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$\"\"$

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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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$\"\"$

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$\"\"$

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Therefore, the point on the curve is $\"\"$ .

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$\"\"$

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The slope intercept form of line equation is $\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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

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$\"\"$

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$\"\"$

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$\"\"$

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Therefore, the tangent line to the curve is $\"\"$ .

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$\"\"$

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The tangent line to the curve $\"\"$ is $\"\"$ .