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

Determine the $y$-intercept(s) of the level curve, where $f\left(x,y\right)=2{e}^{2\sqrt{{x}^{2}+{y}^{2}}}$ and $z=4$.
I started but setting $4=f\left(x,y\right)$ then I solved for $y$ and got $\sqrt{\frac{2ln\left(2\right)}{4}-{x}^{2}}$ and I tried solving for $y=0$. Is there a similar way to do this?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Kitamiliseakekw
So if $z=4$, $f\left(x,y\right)=4$.
Hence forth, $4=2{e}^{2\sqrt{{x}^{2}+{y}^{2}}}$. So yes, you were correct to this.
To find the y-intercepts, $x=0$ since the intercepts are solely on the $y$-axis and you already know that $z=4$.
You now have $4=2{e}^{2\sqrt{{y}^{2}}}$ for $x=0,z=4$.
You cannot solve for the intercepts if $y=0$ because you would be finding the $x$-intercepts instead!
Now, you can solve for $y$