how exactly do you know what the level curves of a function are?

for example: f(x,y)=x^2+y

Question

how exactly do you know what the level curves of a function are? 

for example: f(x,y)=x^2+y

anonymous · Answer

Equate the function to a constant. This equation will describe your curves.

anonymous · Answer

So in your example: 
x^2+y=c
y=c - x^2

anonymous · Answer

so once you set the equation to a constant,"c', you solve for y? plus where can i find like a list of the equations for like a hyperbola and ellipse? 

i set the equation to a constant but i get stuck when it comes to recognizing the graph

anonymous · Answer

You don't have to solve for y, if your function is x^2+y^2, the curves will described by

x^2+y^2=c. You should recognize this being a circle.

anonymous · Answer

here's a small list: http://en.wikipedia.org/wiki/Conic_section#Features