Maths Paper 1, November 2024, question 5.3

The diagram below shows the graph of $f(x)={\displaystyle \frac{a}{x+p}}+q$, with domain $x\in \mathbb{R}$, $x\mathrm{\ne }2$. The vertical asymptote is $x=2$ and the horizontal asymptote is $y=-1$. The graph of $f$ cuts the $y$-axis at $(0;2)$. Calculate the value of $a$.