Vertex is (4, 3) and diretctrix is 3x + 2y – 7 = 0 then equation of latusrectum is

Given that vertex is $\left(4,3\right)$ and the directrix is $3x+2y-7=0$

The latus rectum is a line parallel to the directrix, and it is in the form of $3x+2y+k=0$

The midway between the directrix and latursrectum is passing through the vertex

hence, $3x+2y+\left(\frac{k-7}{2}\right)=0$ passes through the point $\left(4,3\right)$

Hence, 

    $\begin{array}{rcl}12+6+\frac{k-7}{2}& =& 0\\ \frac{k-7}{2}& =& -18\\ k& =& -29\end{array}$

Therefore, the equation of the latusrectum is $3x+2y-29=0$