How to plot an implicit function?

Question

Usually to plot an equation like $y=f(x)$, you do so by using

Plot[f[x],{x,0,10}]

However, my equation takes the form $f(x,y)=0$ and $y$ can't be separated to make an equation like $y=f(x)$. Is there a way to plot the values of $y$ by plotting $f(x,y)$ over $x$.

Answer 1

ContourPlot is probably the solution you are looking for. Here is an example using the function $f(x, y)=x^2 - y^2 - 1$:

f[x_, y_] := x^2 - y^2 - 1
ContourPlot[f[x, y] == 0, {x, -3, 3}, {y, -3, 3}]