If the verex  of a parabola is (4,3) and its directrix is 3x + 2y -7=0, then equation of latus  rectum of the parabola is 

$$\begin{gathered} Given Directrix of parabola is 3x+2y-7=0 \\ and vertex of parabola=(4,3) \\ Latusrectum is parallel to directrix and pas\sin g through focus. \\ Slope of latus rectum =\frac{3}{2} \\ Let equation of latus reactum be y=\frac{-3}{2}x+c \\ Dis\tan ce between vertex to directrix=\frac{1}{2} (Dis\tan ce between latus rectum and directrix ) \\ \Rightarrow \frac{\left|12+6-7\right|}{\sqrt{9+4}}=\frac{1}{2}\frac{\left|{\displaystyle \frac{7}{2}}-c\right|}{\sqrt{1+{\left({\displaystyle \frac{-3}{2}}\right)}^2}} \\ \Rightarrow 22=\left|7-2c\right| \\ \Rightarrow 22=7-2c(\because 2c>7) \\ \Rightarrow 2c=29 \\ \Rightarrow c=\frac{29}{2} \\ Equation of latusrectum is 3x+2y-29=0 \end{gathered}$$