The equations are  and 

The equation is .

Differentiate on each side with respect to .

Product rule of the derivatives : .

The slope of the equation is .

The equation is 

Apply derivative on each side wih respect to .

.

The slope of the equation is .

Two functions are orthogonal if .

Substitute  and  in .

The two functions are orthonogonal to each side.

The functions are  and 

Consider  and .

 and 

  and .

Graph :

Graph the equations   and  :

Observe the graph :

The tangent line to the curve are orthogonal to each other.

The functions are  and 

Consider  and .

 and 

  and .

Graph:

Graph the equations  and :

Observe the graph :

The tangent line to the curve are orthogonal to each other.

Both the tangents are orthogonal to each other.