Explanation

(d)
Since, $y = |x| + c$ and $x^{2} + y^{2} - 8|x| - 9 = 0$ both are symmetrical about $y$-axis for$x > 0,\ y = x + c$. Equation of tangent to circle $x^{2} + y^{2} - 8x - 9 = 0$ which is parallel to $y = x + c$ is $y = (x - 4) + 5\sqrt{1 + 1}$
$\Rightarrow y = x + (5\sqrt{2} - 4)$
For no solution $c > 5\sqrt{2} - 4$,
$\therefore c \in \left( 5\sqrt{2} - 4,\ \infty \right)$