Determine the $y$-intercept(s) of the level curve, where $f(x,y)=2{e}^{2\sqrt{{x}^{2}+{y}^{2}}}$ and $z=4$.

I started but setting $4=f(x,y)$ then I solved for $y$ and got $\sqrt{\frac{2ln(2)}{4}-{x}^{2}}$ and I tried solving for $y=0$. Is there a similar way to do this?

I started but setting $4=f(x,y)$ then I solved for $y$ and got $\sqrt{\frac{2ln(2)}{4}-{x}^{2}}$ and I tried solving for $y=0$. Is there a similar way to do this?