## Similar transformation

Given that $y=ax^2$ is the similar transformation of $y=x^2$, determine the ratio of similitude.

In my solution book, I follow every step, but not the answer.

When $\left\{ \begin{gathered}x'=kx \\ y'=ky \end{gathered} \right.$, $\left\{ \begin{gathered}x=\frac{1}{k}x' \\ y=\frac{1}{k}y' \end{gathered} \right. (2)$

Substituting (2) into $y=x^2$

$\frac{1}{k}y'=\bigg ( \frac{1}{k}x' \bigg )^2$
$y'=\frac {1}{k}(x')^2$
$\therefore k=\frac {1}{a}$

How do you get $k=\frac {1}{a}$