Any line through the point (8,1) is
y−1=m(x−8)
or mx−y+(1−8m)=0.....(1)
If it is a tangent then perpendicular from centre (1,2) is equal to radius √1+4+20=5
∴m−2+(1−8m)√(m2+1)=5
or (−7m−1)2=25(m2+1)
or 49m2+14m+1=25m2+25
or 24m2+14m−24=0
or 12m2+7m−12=0
or 12m2+16m−9m−12=0
(3m+4)(4m−3)=0
∴m=−4/3,3/4.
Putting the values of m in (1), the required tangents are
4x+3y−35=0
and 3x−4y−20=0.