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 - 4 y + 4 = 0 at two distinct points is....

Step-by-step solution

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 3 + 8 - k 5 < 1 11 - k < 5 - 5 < 11 - k < 5 ⇒    k ∈ ( 6 , 16 ) k = 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 Number of values of k = 9 .