Tricky Limit Problem involving e

Question

Find $\lim_{x\rightarrow 0}\exp(-1/(x^2+y^2))$.

I've tried multiplying the power out by the conjugate, which gives me a power of $y^2-x^2/x^4-y^4$, but I still can't figure out how to whittle this down. The most confusing thing to me is that the answer is supposedly $0$. How can $e^\text{anything}$ limit to zero?

EDIT: I should add: I understand the general concept of what the graph looks like, and as the exponent shrinks, the number stretches towards infinity in the x direction. The issue is that I don't know how to actually formally solve this question other than a verbal explanation.

Answer 1

Hint: Think in terms of polar coordinates. $x^2+y^2=r^2$, and use the hint given in the comment by Regret.

Answer 2

Very simple if based on your comments you meant to say $$ \lim_{(x,y) ->0} e^{\frac {- 1} {x^2 + y^2}} = e ^ { \lim_{(x,y)->0} \frac {- 1} {x^2 + y^2}} = e^{-\lim_{(x, y)->0} \frac 1 {x^2+y^2}} = e^{-\infty} = 0 $$