Q95 / 160 · TS EAMCET 2024 (09 May Shift 2) · Mathematics
The equations of the directrices of the ellipse $9 x^2+4 y^2-18 x-16 y-11=0$ are
- Correct answerA$y=2 \pm \frac{9}{\sqrt{5}}$
- B$x=1 \pm \frac{6}{\sqrt{5}}$
- C$x=2 \pm \frac{9}{\sqrt{5}}$
- D$y=1 \pm \frac{6}{\sqrt{5}}$
Solution
$9 x^2+4 y^2-18 x-16 y-11=0$
$\Rightarrow \frac{(x-1)^2}{4}+\frac{(y-2)^2}{9}=1 \Rightarrow e=\sqrt{\frac{9-4}{9}}=\frac{\sqrt{5}}{3}$
Vertex $(h, k)=(1,2)$ Equations of the directrices, $y-k= \pm \frac{b}{e}$ $y-2= \pm \frac{9}{\sqrt{5}} \Rightarrow y=2 \pm \frac{9}{\sqrt{5}} .$
Vertex $(h, k)=(1,2)$ Equations of the directrices, $y-k= \pm \frac{b}{e}$ $y-2= \pm \frac{9}{\sqrt{5}} \Rightarrow y=2 \pm \frac{9}{\sqrt{5}} .$
Hence, the correct answer is option: 'A'.