If the circle x 2 + y 2 - 4 x - 8 y - 5 = 0 intersects the line 3   x - 4   y - m = 0 in two…

If the circle is intersecting line $3x-4y=m$ at two distinct points then we can say that

Radius $>$ length of perpendicular from center to the given line

Perpendicular distance, $P=\frac{\left|a{x}_1+b{y}_1+c\right|}{\sqrt{a^2+b^2}}, r=\sqrt{g^2+f^2-c}$

$\Rightarrow \sqrt{4+16+5}>\frac{\left|3\left(2\right)-4\left(4\right)-m\right|}{\sqrt{9+16}}$

$\Rightarrow \left|m+10\right|<25$

$\Rightarrow m+10<25 \text{or} m+10>-25$

$\Rightarrow -35<m<15$

There are $49$ integers between $-35 \& 15$

So, the correct answer is $49$.