$\"\"$

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

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$\"\"$

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Use the power rule of derivative : $\"image\"$

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Use the constant rule of derivative : $\"image\"$

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

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$\"\"$

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

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

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$\"\"$

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Use the power rule of derivative : $\"image\"$

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

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$\"\"$

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

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