Implicit function and polynomials

Question

Can someone give me an example what is the difference between an implicit function and curve with polynomials as coordinate system?

I am learning basic math concepts and I do not understand those two concepts.

So for my homeworks I supplied this answer as polynomials and I got answer that this is an implicit function, and not the curve with polynomials as coordinate functions.

my answer as image

Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. — José Carlos Santos, Jan 21 '18 at 12:26
What do you mean with "with polynomials as coordinate system"? — 57Jimmy, Jan 21 '18 at 12:27

score 0 · Accepted Answer · answered Jan 21 '18 at 13:25

An example of a curve with polynomials as its coordinate functions is: $$ x(t) = t \quad ; \quad y(t) = t^2 $$ Curve equations of this type are called parametric equations, and the variable $t$ is called the parameter. See here.

This same curve can also be described by the equation $$ x^2 - y = 0 $$ We would say that this is the implicit equation of the curve. See here.

Implicit function and polynomials

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