dirac delta function limit form equality

Question

Show that $$\lim_{y\to\infty}\frac{1}{\pi}\frac{y}{y^2+x^2} = \delta(x)$$

I do not know where the $\pi$ arise.

Answer 1

The constant $\pi$ is to normalize the area under the curve to unity.

$$\int_{-\infty}^{\infty}{\frac{y}{y^2+x^2}}dx = \pi$$