Q96 / 160 · AP EAMCET 2018 (22 Apr Shift 2) · Mathematics
The equations of the latusrectum of the ellipse $9 x^2+4 y^2-18 x-8 y-23=0$ are
- A$x=-1 \pm \sqrt{5}$
- Correct answerB$y=1 \pm \sqrt{5}$
- C$x=1 \pm \frac{2 \sqrt{5}}{3}$
- D$y=2 \pm \sqrt{5}$
Solution
Equation of given ellipse
$$
\begin{aligned}
& 9 x^2+4 y^2-18 x-8 y-23=0 \\
& \Rightarrow \quad 9(x-1)^2+4(y-1)^2=36 \\
& \Rightarrow \quad \frac{(x-1)^2}{4}+\frac{(y-1)^2}{9}=1 \\
&
\end{aligned}
$$
Equation of latus rectum is
$$
\begin{array}{lrl}
\Rightarrow & y-1 & = \pm 3 \frac{\sqrt{5}}{3} \\
\Rightarrow & y & =1 \pm \sqrt{5}
\end{array}
$$
Hence, the correct answer is option: 'B'.