# The circle $x^2+y^2=4x+8y+5$ intersects the line $3x-4y=m$ at the two distinct points if

$\begin{array}{1 1}(A)\;-35 < m< 15 \\(B)\;15 < m < 65 \\(C)\;35 < m < 85 \\(D)\;-85 < m < -35 \end{array}$

Circle $x^2+y^2-4x-8y-5=0$
Centre $=(2,4)$
Radius $=\sqrt {4+16+5}$
$\qquad= \sqrt {25}$
$\qquad=5$
If circle is intersecting line $3x-4y=m$ at two distinct points.
length of perpendicular from centre to the line < radius
$=> \large\frac{|6-16-m|}{5}$$< 5$
$=> |10+m| <25$
$=> -25 < m+10 <25$
$=> -35 < m <15$
Hence A is the correct answer.