In my mind I'm confusing an implicit function f(x,y) with function z=f(x,y). One of the characteristics of an implicit is that it can let us represent a two-part function in one expression. For instance, consider the equation of a circle:

**x^2 + y^2 = c^2**[one part function] =>

**y=+/- sqrt(c^2-x^2)**[two part function]. Are there some other advantages of an implicit function? In case of an implicit function,

__y is a dependent variable (function of x)__and x is independent.

Isn't function in space also represented as z=f(x,y) where 'z' is determined using x and y coordinates? Is y an independent variable or function of x as it is for an implicit function in x-y plane? Perhaps, both x and y are functions of some other parameter such as 'c'.

I'm sorry if my query(ies) is too confusing. Please let me know if you need some clarification about any part. Please help me with it. Thank you.

Regards

PG