The numbers of integral values of k for which the line, 3 x + 4 y = k intersects the circle, x 2 + y 2 - 2 x…

If distance from center to line is less than radius then line cut circle at two distinct point.

Center of circle $(1,2), r=1$

$\left|\frac{3+8-k}{5}\right|<1$

$\left|11-k\right|<5$

$-5<11-k<5\Rightarrow k\in (6,16)$

$k=7,8,9,10,11,12,13,14,15$

Number of values of $k=9$.