The functions are  and 

Find intersection points.

Substitute  in .

At  ,

At  ,

The intersection points are 

The functions is .

Differentiate with respect to .

Use the power rule of derivative :

Use the constant rule of derivative :

The slope .

At point  slope is .

The slope point form is .

Substitute  in .

At point  the tangent line is 

The slope .

At point  slope is .

The slope point form is .

Substitute  in .

At point  the tangent line is 

The functions is .

Differentiate with respect to .

Use the power rule of derivative :

The slope .

At point  slope is .

The slope point form is .

Substitute in .

At point  the tangent line is 

The slope .

At point  slope is .

The slope point form is .

Substitute  in .

At point  the tangent line is 

Graph:

Observe from the graph :

Both the tangents are orthogonal to each other.

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