Let a point P be such that its distance from the point (5, 0) is...

Let point is $\left(h, k\right)$

So, $\sqrt{{\left(h - 5\right)}^{2} + {k}^{2}} = 3\sqrt{{\left(h + 5\right)}^{2} + {k}^{2}}$

$8{x}^{2} + 8{y}^{2} + 100x + 200 = 0$

${x}^{2} + {y}^{2} + \dfrac{25}{2}x + 25 = 0$

${r}^{2} = \dfrac{{\left(25\right)}^{2}}{{4}^{2}} - 25$

$4{r}^{2} = \dfrac{{25}^{2}}{4} - 100$

$4{r}^{2} = 156 . 25 - 100$

$4{r}^{2} = 56 . 25$

After round off $4{r}^{2} = 56$