(a) If the sum of the roots of the quadratic equation ${\mathrm{ky}}^2-11\mathrm{y}+\left(\mathrm{k}-23\right)=0$ is $\frac{13}{21}$ more than the product of the roots, then find the value of $\mathit{k}$.
OR
(b) If $\mathit{x}=-2$ is the common solution of quadratic equations $\mathrm{a}{\mathit{x}}^2+\mathit{x}-3\mathrm{a}=0$ and ${\mathit{x}}^2+\mathit{b}\mathit{x}+\mathit{b}=0$, then find the value of ${\mathrm{a}}^2\mathrm{b}$.