  In this article the Diophantine equations of the form $x^{2}-8C_{n}xy+
16y^{2}=\pm2^{r}$, $x^{4}-8C_{n}x^{2}y+ 16y^{2}=\pm2^{r}$ and
$x^{2}-8C_{n}xy^{2}+ 16y^{4}=\pm2^{r}$ are taken into consideration for the
investigations of existence of any positive integer solutions. Furthermore, the
solutions are manifested in terms of the balancing, Pell and Lucas-Pell
numbers.
