# Deriving the corresponding Location - Scale Family

I am little confused about deriving the location-scale family of these three distributions.

(a) Let $$f(x)=\frac{1}{\pi (1+x^2)}$$, $$-\infty. I have no idea how to go about this.

(b) Gamma$$(\alpha_0,\beta)$$ distributions, where $$\alpha_0$$ forms a scale family.

My attempt:

The density of a Gamma$$(\alpha_0,\beta)$$ distribution is $$f(x, \alpha_0) = \frac{1}{\Gamma(\alpha_0)}x^{\alpha_0 - 1}e^{x}, \quad x > 0; \alpha_0 > 0, \tag{1}$$

Can anyone give explanation on how the gamma distribution forms a scale family.

(c) N$$(1,\sigma^2)$$ distributions does not form a scale family. How do I show this?