Let $V\subset\mathbb{P}^5$ be the Veronese surface and let $X\subset\mathbb{P}^6$ be the cone over it. Since $X$ is $\mathbb{Q}$-factorial there are two integers $a,b$ such that $aK_X = \mathcal{O}_X(b)$.

Furthermore, if $f:Y\rightarrow X$ is the blow-up of the vertex then $Y$ is smooth and we may write $K_Y = f^{*}K_{X}+dE$, where $E$ is the exceptional divisor, and $d$ is a rational number.

How can I determine the numbers $a,b,d$ ?