Every-equation-of-x-y-has-a-curve-in-a-plane-Does-every-curve-in-a-plane-has-an-equation-

Question Number 3693 by Rasheed Soomro last updated on 19/Dec/15

E v e r y e q u a t i o n o f x, y h a s a c u r v e i n a p l a n e .

D o e s e v e r y c u r v e i n a p l a n e h a s a n e q u a t i o n ?

Commented by 123456 last updated on 19/Dec/15

i think the answer is yes

lets f : R^{2} \to R

a curvw can be given by

f (x, y) = k, k \in R

what i think that can happen is that

the function f (x, y) is so hard to be given

in some cases

Commented by Rasheed Soomro last updated on 19/Dec/15

I f w e d r a w a c u r v e w i t h o u r h a n d i n

a p l a n e, m u s t i t h a v e a n e q u a t i o n (t h e o r e t i c a l l y) ?

Commented by 123456 last updated on 19/Dec/15

yes, can simple take

f (x, y) = {\begin{cases} 0 & (x, y) \in A \\ 1 & (x, y) \notin A \end{cases}

and drawn

f (x, y) = 0

A \subset R^{2}

its look fine, but it depends of how you

describe it, the circle of radius r with

center in (0, 0) can be given in cartesian

by

x^{2} + y^{2} = r^{2}

or in polar by

r (θ) = r

note that in the second case its more

simple, so there are curve that can be

easy given in one coordinate system than

other

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