Recovering beta parameters from a scaled variable

Suppose $X\sim\text{Beta}(a,b)$ with $a,b$ unknown, and for some constants $c,d$ the variable $Y=cX+d$ has support $[-0.02,0.04]$, mean $\tfrac{1}{400}$ and variance $\tfrac{3}{32000}$. Determine $a-b$.

$-2$. Matching the support gives $Y=0.06X-0.02$, so $E[X]=\tfrac38$ and $\operatorname{Var}(X)=\tfrac{5}{192}$. Since a beta variance equals $\tfrac{\mu(1-\mu)}{a+b+1}$, we get $\tfrac{15/64}{a+b+1}=\tfrac5{192}$, so $a+b=8$; with $\tfrac{a}{a+b}=\tfrac38$ this gives $a=3$, $b=5$.