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JEE Main 20207 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
7 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Ellipse

JEE Main 2020 · 7 January · Morning Shift · Mathematics · Ellipse

If the distance between the foci of an ellipse is 6 and the...

If the distance between the foci of an ellipse is 66 and the distance between its directrix is 12,12, then the length of its latus rectum isIf the distance between the foci of an ellipse is 6 and the distance between its directrix is 12, then the length of

Options

  1. A3\sqrt{3}
  2. B323\sqrt{2}
  3. C32\dfrac{3}{\sqrt{2}}
  4. D232\sqrt{3}

Correct answer

B. 323\sqrt{2}

Step-by-step solution

If the distance between the foci of an ellipse is 6 and the distance between its directrix is 12, then the length ofGiven, 2ae=62ae = 6 and 2ae=12\dfrac{2a}{e} = 12, directrices are x=±aex = \pm \dfrac{a}{e}

So, ae=6\dfrac{a}{e} = 6

Now, using the formula for eccentricity of an ellipse

⇒b2=a2−a2e2=18−9=9⇒ {b}^{2} = {a}^{2} - {a}^{2}{e}^{2} = 18 - 9 = 9

⇒L.R.=2b2a=2×932=32⇒ L . R . = \dfrac{2{b}^{2}}{a} = \dfrac{2 \times 9}{3\sqrt{2}} = 3\sqrt{2}

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