If the vertex of the parabola is (4, 3) and its directrix is $3x+2y-7=0$ then the equation of its latusrectum of the parabola is

given vertex A = (4, 3)
Equation of directrix in $3x+2y-7=0\stackrel{ }{\to }\left(1\right)$
Equation of latusrectum is $3x+2y+k=0\stackrel{ }{\to }\left(2\right)$  
(Directrix//latus rectum)
Now 
Dist from A to (1) = Dist from A to (2)
$\frac{\left|3\left(4\right)+2\left(3\right)-7\right|}{\sqrt{9+4}}=\frac{\left|3\left(4\right)+2\left(3\right)+k\right|}{\sqrt{9+4}}$

$11=\left|18+k\right|$

$18+k=11\left(or\right)18+k=-11$

$k=-7\left(or\right)k=-29$

$\therefore$ Equation of latus rectum is $3x+2y-29=0$