Explanation

(a)
Given, $x^{2} - xy + y^{2} - 4x - 4y + 16 = 0$
$\Rightarrow \ \ x^{2} - (y + 4)x + y^{2} - 4y + 16 = 0$
For real $x,\ (y + 4)^{2} - 4\left( y^{2} - 4y + 16 \right) \geq 0$
$\Rightarrow \ - 3y^{2} + 24y - 48 = 0$
$\Rightarrow \ \ \ y^{2} - 8y + 16 = 0$
$\Rightarrow \ \ (y - 4)^{2} = 0\ \ \ \Rightarrow \ \ y = 4$
$\therefore$ From given equation $x = 4$
$\Rightarrow \ \ \ (x,\ y) = (4,\ 4)$