The largest and smallest distances of a satellite from centre of planet are given as  $R_{\max }$ and $R_{\min }$  respectively. At these two positions, speeds are given as  $v_{\min }$ and $v_{\max }$ respectively. The time period of revolution of the satellite is T. If  '$a$' and '$b$' are semi major and semi minor axes, then

Hence current through $6\Omega$  is $\frac{2}{12}=\frac{1}{6}A$  and current through $3\Omega$  is   $\frac{2}{6}=\frac{1}{3}A$

$R_{\max }=a+ae{R}_{\min }=a-ae$

$a=\frac{R_{\max }+R_{\min }}{2};b=\sqrt{R_{\max }.R_{\min }}$

$\therefore v_{\max }=\sqrt{GM(\frac{2}{R_{\min }}-\frac{1}{a})}=\sqrt{\frac{GM(2a-R_{\min })}{a{R}_{\min }}}$

$=\sqrt{\frac{GM{R}_{\max }}{a{R}_{\min }}}\mathrm{...............}\left(1\right)$

as $v_{\min }=\sqrt{GM(\frac{2}{R_{\max }}-\frac{1}{a})}=\sqrt{\frac{GM(2a-R_{\max })}{a{R}_{\max }}}$

$=\sqrt{\frac{GM{R}_{\min }}{a{R}_{\max }}}\mathrm{...............}\left(2\right)$

Multiplying (1) and (2)

or$\sqrt{v_{\max }{v}_{\min }}=\sqrt{\frac{GM}{a}}=a\sqrt{\frac{GM}{a^3}}=\frac{2\pi a}{T}asT=2\pi \sqrt{\frac{a^3}{GM}}$

$\therefore a=\frac{T}{2\pi }\sqrt{v_{\max }{v}_{\min }}$