Question

Observe the following lists, In List-I there are ellipses and in List -II their foci
are given
List -I List -II
A $\frac{x^2}{16}+\frac{y^2}{12}=1$ $(0,\pm 5)$

B $\frac{x^2}{11}+\frac{y^2}{36}=1$ $(\pm 2,0)$

C $\frac{x^2}{7}+\frac{y^2}{16}=1$ $(0,\pm \sqrt{5})$

D. $\frac{x^2}{9}+\frac{y^2}{4}=1$ $(0,\pm 3)$
$(\pm \sqrt{5},0)$
The correct match for List-I from List-II is

• A. $ABCD$
  $2154$
• B. $ABCD$
  $5412$
• C. $ABCD$
  $3145$
• D. $ABCD$
  $2145$

Answer 1

The correct option is D $ABCD$

$2145$
$\left(A\right)e^2=\frac{16-12}{16}=\frac{1}{4}$
$e=\frac{1}{2}$
$(\pm qe,0)$
$(\pm \frac{1}{2}\times 4,0)$
$=(\pm 2,0)$
$\left(B\right)e^2=\frac{36-11}{36}$
$e=\frac{5}{6}$
$(0,\pm be)$
$(0,\pm 5)$
$\left(C\right)e^2=\frac{16-7}{16}$
$e=\frac{3}{4}$
$(0,\pm be)$
$(0,\pm \frac{3}{4})$
$(0,\pm 3)$
$\left(D\right)e^2=\left(\frac{9-4}{9}\right)$
$e=\frac{\sqrt{5}}{3}$
$(\pm ae,0)$
$=(\pm \sqrt{5},0)$