The equation of the latus recta of the ellipse $9x^{2}+4^{2}-18x-8y-23=0$ are ;

equation of ellipse is ${ 9x }^{ 2 }+{ 4y }^{ 2 }-18x-8y-23=0$

$\Rightarrow (9x^{ 2 }-18x+9)+(4y^{ 2 }-8y+4)-23-9-4=0$

$\Rightarrow 9(x-1)^{ 2 }+4(y-1)^{ 2 }=36$

$\Rightarrow \cfrac { (x-1)^{ 2 } }{ 4 } +\cfrac { (y-1)^{ 2 } }{ 9 } =1$

So, equation of latus recta is $(y-1)=\pm be$

$y=1\pm \sqrt { b^{ 2 }-a^{ 2 } } \Rightarrow y=1\pm \sqrt { 5 }$