A) \[y=\pm \text{ }\sqrt{5}\]
B) \[x=\pm \text{ }\sqrt{5}\]
C) \[y=1\pm 5\]
D) \[x=-1\pm \sqrt{5}\]
Correct Answer: C
Solution :
Equation of ellipse is \[9{{x}^{2}}+4{{y}^{2}}-18x-8y-23=0\] \[\Rightarrow \]\[9({{x}^{2}}-2x+1)-9+4({{y}^{2}}-2y+1)\] \[-4-23=0\] \[\Rightarrow \]\[9{{(x-1)}^{2}}+4{{(y-1)}^{2}}=36\] \[\Rightarrow \]\[\frac{{{(x-1)}^{2}}}{4}+\frac{{{(y-1)}^{2}}}{9}=1\] Here, \[a<b\] Also, \[e=\sqrt{1-\frac{4}{9}}=\sqrt{\frac{5}{9}}=\sqrt{\frac{5}{3}}\] \[\therefore \]Equations of latusrectum are \[y-1=\pm \,3.\frac{\sqrt{5}}{3}\] \[\Rightarrow \] \[y=1\pm \sqrt{5}\]
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