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If S and S' Are Two Foci of the Ellipse X 2 a 2 + Y 2 B 2 = 1 and B is an End of the Minor Axis Such that ∆Bss' is Equilateral, Then Write the Eccentricity of the Ellipse. - Mathematics

If S and S' are two foci of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and B is an end of the minor axis such that ∆BSS' is equilateral, then write the eccentricity of the ellipse.

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Solution

\[\text{ We know that the focal distance of a point B }(0, b) \text{ is } a \pm e . 0 = a\]
\[\text{ i . e } . SB = SB' = a\]
`therefore SB + S B^' = 2a `
 `"Since" ∆ {BSS}^' \"is equilateral, we have":`
`SB = S S^' = S^' B = 2ae`
\[ \Rightarrow 2ae + 2ae = 2a\]
\[ \Rightarrow 4ae = 2a\]
\[ \Rightarrow e = \frac{2}{4}\]
\[ \Rightarrow e = \frac{1}{2}\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 26 Ellipse
Q 7 | Page 27
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