$\"\"$

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The $\"\"$ and $\"\"$ .

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Find intersection points.

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

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$\"\"$

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$\"\"$ .

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Solutions for the equation is $\"\"$ .

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The intersection points is $\"\"$ .

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$\"\"$

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The curve equation is $\"\"$ .

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

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$\"\"$

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At point $\"\"$ , slope of the tangent line is $\"\"$ .

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The point-slope form of line equation is $\"\"$ .

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Substitute $\"\"$ is $\"\"$ and $\"\"$ in the point slope form..

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$\"\"$

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The tangent line equation is $\"\"$ .

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$\"\"$

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

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The point-slope form of line equation is $\"\"$ .

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Substitute $\"\"$ is $\"\"$ and $\"\"$ in point slope form.

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$\"\"$

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The tangent line equation 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 perpendicular to each other.

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The two curve equations are orthogonal to each other.

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$\"\"$

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The two curve equations are orthogonal to each other.