If the circle x 2 + y 2 = 4 x + 8 y + 5 intersects the line 3 x - 4 y = m at two distinct points, then the number of possible integral values of m is equal to

Step-by-step solution

The equation of the circle is x 2 + y 2 - 4 x - 8 y - 5 = 0 Its centre is 2 , 4 and radius is 4 + 16 + 5 = 5 units It the circle intersects the line 3 x - 4 y = m at two distinct points, then the length of the perpendicular from the centre is less than the radius i.e., 6 - 16 - m 5 < 5 ⇒ 10 + m < 25 ⇒ - 25 < m + 10 < 25 ⇒ - 35 < m < 15 Hence, the total number of integral values of m is 49