If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12 , then the…

If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12, then the length of its latus rectum is
  1. 3
  2. 32
  3. 32
  4. 23

Solution

Given, 2ae=6 and 2ae=12, directrices are x=±ae

So, ae=6

Now, using the formula for eccentricity of an ellipse

⇒b2=a2-a2e2=18-9=9

⇒L.R.=2b2a=2×932=32

Asked in: JEE Main 2020 (07 Jan Shift 1)

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