$\"\"$

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The functions are $\"\"$ and $\"\"$ .

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Find intersection points.

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

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$\"\"$

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

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imaginary oots are not constder ,hence $\"\"$ and $\"\"$ .

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At $\"\"$ ,

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$\"\"$

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At $\"\"$ ,

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$\"\"$

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

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$\"\"$

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The functions is $\"\"$ .

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Differentiate on each side with respect to $\"image\"$ .

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$\"\"$

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$\"\"$

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At point $\"\"$ , $\"\"$ slope is $\"\"$ .

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The slope point form is $\"\"$ .

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

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$\"\"$

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At point $\"\"$ the tangent line is $\"\"$ .

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$\"\"$

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The functions is $\"\"$ .

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Differentiate on each side with respect to $\"image\"$ .

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$\"\"$

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$\"\"$ .

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The slope $\"\"$ .

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At point $\"\"$ , $\"\"$ slope is $\"\"$ .

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The slope point form is $\"\"$ .

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

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$\"\"$

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At point $\"\"$ the tangent line is $\"\"$ .

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$\"\"$

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Graph:

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$\"\"$

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Observe from the graph :

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Both the tangents are orthogonal to each other.

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$\"\"$

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$\"\"$

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