The correct option is D When L1 is at a distance of 1 from the centre, its equation is x+3y−11−√10=0
Given circle is x2+y2−4x−6y+4=0
C=(2,3), r=3
Diameter is 3x−y−3=0
The largest chord is diameter and two diameter always bisect each other.
Checking the equations
x+3y−11=0 and x−3y+8=0
Diameter passes through the centre (2,3), so
2+9−11=02−9+8=1≠0
Therefore x+3y−11=0 can be equation of diameter.
The chord which is bisected by the given diameter is perpendicular to it, so the equation of chord is
x+3y+λ=0
Distance from centre is 1, so
|11+λ|√10=1⇒λ=−11±√10
Hence, the required equation of chord are
x+3y−11+√10=0x+3y−11−√10=0