The correct option is A 165
The given equation of the parabola can be written as
(x−2)2+(y−4)2=(4x−3y+12√(4)2+(−3)2)2
∴ The coordinates of focus are (2,4) and the equation of directrix is 4x−3y+12=0.
The distance of the focus from the directrix
=∣∣
∣
∣∣4(2)−3(4)+12√42+(−3)2∣∣
∣
∣∣=85
∴ The length of latus rectum
=2× distance of the focus from the directrix
=2×85=165