Conditional moments given X for a joint density

Let $X$ and $Y$ have the joint probability density function

$$f(x,y)=\begin{cases}2, & 0\le x\le y\le1,\ 0, & \text{otherwise.}\end{cases}$$

Let $a=E\left(Y|X=\frac12\right)$ and $b=Var\left(Y|X=\frac12\right)$. Then $(a,b)$ is