Question

.Observe the following lists for the ellipse $16x^2+9y^2=144$
List-I List-II
A. Eccentricity 1 . $(0,\pm \sqrt{7})$
B. Foci 2. $y=\pm \frac{16}{\sqrt{7}}$
C. Latus rectum 3. $(\pm \sqrt{7},0)$
D. Equation of directrieces 4. $\frac{\sqrt{7}}{4}$
5. $x=\pm \frac{16}{\sqrt{7}}$
6. $\frac{9}{2}$

The correct match for list-l from list-ll is

• A. A B C D
  4 5 1 6
• B. A B C D
  4 1 6 2
• C. A B C D
  4 3 6 5
• D. A B C D
  4 1 3 5

Answer 1

Answer: (B)

A B C D

4 1 6 2
$\left(A\right)\frac{x^2}{9}+\frac{y^2}{16}=1$
$e^2=\frac{16-9}{16}$
$e=\frac{\sqrt{7}}{4}$
$\left(B\right)(0,\pm be)$
$=(0,\pm 4\times \frac{\sqrt{7}}{4})$
$=(0,\pm \sqrt{7})$

$\left(C\right)$ $latusractum=\frac{2a^2}{b}$

$=2\times 9/4=9/2$
$\left(D\right)y+\frac{b}{e}=0$

$y=\pm \frac{16}{\sqrt{7}}$