how do we interpret an equation for example
x^{2} + x*y + y^{2} = 0 or
x^{2}y + x + y^{2} = 0
are these just curves on the x and y axis.
And if these are curves what are they curves of?
I want a physical interpretation of the above equations
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how do we interpret an equation for example
x^{2} + x*y + y^{2} = 0 or
x^{2}y + x + y^{2} = 0
are these just curves on the x and y axis.
And if these are curves what are they curves of?
I want a physical interpretation of the above equations
Your first description is correct. These are just curves in the (x,y) plane. There is no physical interpretation unless x and y are defined as physical variables.
For interpretion these equation there is no need to know the variables -knowing the just change the coordinations of points not the shape-for example any equation like x^{2}+ x+a=y will be kind of parabola,equation like x-a=y will be just a line , x^{3} + x^{2}+x=y will be two reversed side(each side is a half parabola) -point coordination located on each half would be (x,y)-(-x,-y)---if equation is x^{2}=y^{2} it is (V) form starts from o point (0,0) so on i will put chart here as soo as i can but in mean time i hope it would be useful
It might be helpful to think of it as the point where the 2D surface defined by f(x, y) = x^2 + xy + y^2 crosses the plane defined by f(x, y) = 0. Of course, that's just one way of picturing it. I'll agree with mathman though that it doesn't really mean anything physical unless you know what x and y are.
I can not understand your point magimaster ,every equation has its own shape that won`t change even if you define numbers for it-if you give me equation i will tell you how its shape would be before you caculate that with coordinations-so tell me again what is your point????
If you can't see what I mean, then my point would be of no use to you.
Also, your description of functions having some implicit shape like "parabola", etc. is an oversimplification. What shape does have? Basically, the shapes that can be easily classified are only a tiny fraction of the possibilities. Besides that, changing the coordinates can change the shape. Circles can become ellipses or lines with relatively simple changes, just for one example.