Observe the following lists for the ellipse $16 x^{2} + 9 y^{2} = 144$

COLUMN - I COLUMN - II
A) Eccentricity p) $(0, \pm \sqrt{7})$
B) Foci q) $y = \pm \frac{16}{\sqrt{7}}$
C) Latus rectum r) $(\pm \sqrt{7}, 0)$
D) Equation of directrieces s) $\frac{\sqrt{7}}{4}$
t) $\frac{9}{2}$
A B C D
1 s p t q
2 p q r s
3 s t p q
4 t s p q

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answer is A.

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Detailed Solution

equation of the ellipse is $\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1$
A) eccentricity $e = \sqrt{\frac{16 - 9}{16}} = \frac{\sqrt{7}}{4}$
B) foci are $(0, \pm be) = (0, \pm \sqrt{7})$
C) L.L.R $= \frac{2 a^{2}}{b} = \frac{2 .9}{4} = \frac{9}{2}$
D) equation of directrices are $y = \pm \frac{b}{e} \Rightarrow y = \pm \frac{16}{\sqrt{7}}$

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