What is the degree of dissociation of weak acid HA (C = 0.1 M) in presence of strong acid HB (C = 0.1 M)? Given : $K_a=$(weak acid )$={10}^{-6}$

$\begin{array}{ccc}\mathrm{HA}\rightleftharpoons & {\mathrm{H}}^{+}+& A^{-}\\ \mathrm{C}& 0& 0\\ C(1-\alpha )& \mathrm{C\alpha }& \mathrm{C\alpha }\end{array}$                 Weak acid

$$\begin{gathered} \mathrm{HB}⟶{\mathrm{H}}^{+}+{\mathrm{B}}^{-} \\ \begin{array}{lcc}0.1& 0& 0\\ 0& 0.1& 0.1\end{array} \end{gathered}$$                            strong acid

Now, with the following formula,

$\begin{array}{l}{K}_a=\frac{\left[\mathrm{H}\right]\left[{\mathrm{A}}^{-}\right]}{\left[\mathrm{HA}\right]}\\ {10}^{-6}\times \left(\mathrm{HA}\right]=\left[0.1\right]\left[{\mathrm{A}}^{-}\right]\\ {10}^{-6}\times C(1-\alpha )=\left[0.1\right]\left[\mathrm{C\alpha }\right]\\ (1-\alpha )\approx 1\\ {10}^{-6}=\left(0.1\right)\cdot \alpha \\ \alpha ={10}^{-5}\end{array}$