The origin shifted to (1, 2) then the equation $y^2–8x–4y+12=0$ changes as $Y^2=4aX$ then a =

$$\begin{gathered} \mathrm{Given} \mathrm{origin} \mathrm{shifted} \mathrm{to} \mathrm{the} \mathrm{point} (\mathrm{h},\mathrm{k})=(1,2) \\ \mathrm{Given} \mathrm{original} \mathrm{equation} \mathrm{is} {\mathrm{y}}^2-8\mathrm{x}-4\mathrm{y}+12=0 \\ \mathrm{Now} \mathrm{transformed} \mathrm{equation} \mathrm{is} \\ {(Y+2)}^2-8(X+1)-4(Y+2)+12=0 \\ \Rightarrow Y^2+4+4Y-8X-8-4Y-8+12=0 \\ \Rightarrow Y^2-8X=0 \\ \Rightarrow Y^2=8X \\ \mathrm{Compare} \mathrm{with} Y^2=4aX \mathrm{then} 4\mathrm{a}=8\Rightarrow \mathrm{a}=2 \end{gathered}$$