Verified Solution • 2025–26 Session moderate

QJEEM20Ma4c24: JEE Main 2020 Mathematics - Class 11 JEEM20Ma4c24 Solution: If the distance between the foci of an ellipse is 6 and the…

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is :

Multiple Choice Options

  • A 3\sqrt 3
  • B 323\sqrt 2
  • C 32{3 \over {\sqrt 2 }}
  • D 232\sqrt 3

Step-by-Step Verified Solution

Distance between foci = 2ae = 6

⇒\Rightarrow ae = 3 .....(1)

Distance between directrices = 2ae{{2a} \over e} = 12

⇒\Rightarrow ae{a \over e} = 6 .....(2)

from (1) and (2)

a2 = 18

also a2e2 = 9

⇒\Rightarrow 18e2 = 9

⇒\Rightarrow e2 = 12{1 \over 2}

We know e2 = 1 - b2a2{{{b^2}} \over {{a^2}}}

∴\therefore 12{1 \over 2} = 1 - b2a2{{{b^2}} \over {{a^2}}}

⇒\Rightarrow b2 = 9

∴\therefore Length of latus rectum = 2b2a{{2{b^2}} \over a}

= 2×918{{2 \times 9} \over {\sqrt {18} }}

= 323\sqrt 2

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