Mathematics - Circle Question with Solution | TestHub

Let ${\mathrm{k}}_1,{\mathrm{k}}_2$ be two integers such that $(\mathrm{n}-\mathrm{a})!=(\mathrm{n}-\mathrm{b})!,2\mathrm{a}+\mathrm{b}+1={\mathrm{k}}_1\mathrm{n}+{\mathrm{k}}_2\forall \mathrm{n}$ where $\mathrm{a}<\mathrm{b}\le \mathrm{n}$ and $\mathrm{a},\mathrm{b},\mathrm{n}\in \mathrm{N}$. Let P and Q be two points on the curve $\mathrm{y}={\log }_{1/2}\left(\mathrm{x}+{\mathrm{k}}_2/2\right)+{\log }_2\left(\sqrt{4{\mathrm{x}}^2+4{\mathrm{k}}_2\mathrm{x}+{\mathrm{k}}_1+{\mathrm{k}}_2}\right)$. Point P also lies on the circle ${\mathrm{x}}^2+{\mathrm{y}}^2={\mathrm{k}}_1{}^3-2{\mathrm{k}}_2$, however Q lies inside the circle such that its abscissa is an integer then