NIMCET 2019 Question Paper with solutions

Question : 31 of 120

Marks: +1, -0

If S and S'' are foci of the ellipse

x^2/a^2

y^2/b^2

= 1, B is the end of the minor axis a tr and BSS'' is an equilateral triangle, then the eccentricity of the ellipse is

Solution:

Since, we know that

x^2/a^2+y^2/b^2=1

SS'=2ae

OB=b

Given, BSS' is an equilateral triangle.

∴\;\;OB=√3/2SS'

b=√3/2\;2ae⇒b/a=√3e

We know

e^2=1-b^2/a^2

e^2=1-3e^2

4e^2=1

e^2=1/4

⇒e=1/2

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