Deriving the Witch of Agnesi Curve

[IvanCow]

Hello,
I have encountered an exercise in my differential geometry book: to derive the parametrisation and the cartesian equation of the curve witch of Agnesi.

To see how it is constructed please see:

http://en.wikipedia.org/wiki/Witch_of_Agnesi"

How would one derive the results? I am lost. Please help. Thanks.

 

[JSuarez]

From the geometric construction and Phytagora's theorem.