If ax+by−3=0 is the equation of the shortest chord of the circle (x−3)2+(y−4)2=4 passing through the point (2,3), then |a+b| is
The shortest chord through a point is always perpendicular to the line joining the center and the point i.e. the point will be the midpoint of the chord
Slope of line joining the center and point is
4–33–2=1
Slope of ax+by–3=0 is −1
⟹−ab=−1⟹a=b
Also (2,3) lies on the chord
⟹2a+3b–3=0
⟹5a=3
⟹a=35=b
|a+b|=65