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Chemistry NCERT Exemplar Solutions Class 12th Chapter Five Conic Sections Ncert Solutions Maths class 11th Maths Class 11th

Let E₁ : $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is:

Option 1 -

$\frac{- 1 + \sqrt[]{5}}{2}$

Option 2 -

$\frac{- 1 + \sqrt[]{3}}{2}$

Option 3 -

$\frac{- 1 + \sqrt[]{8}}{2}$

Option 4 -

$\frac{- 1 + \sqrt[]{6}}{2}$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 1

Detailed Solution:

$E_{1} : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

$e_{1}^{2} = 1 - \frac{b^{2}}{a^{2}}$ -(i)

Let $E_{2} : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{B^{2}} = 1$

B > a

$e_{2}^{2} = 1 - \frac{a^{2}}{B^{2}} a n d g i v e n B e_{2} = b$

$e^{2} = \frac{3 - \sqrt[]{5}}{2} = {(\frac{\sqrt[]{5} - 1}{2})}^{2}$

$\Rightarrow e = \frac{\sqrt[]{5} - 1}{2}$

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Slope of axis = $\frac{1}{2}$

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Let E₁ : $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is:

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Let E1 : x 2 a 2 + y 2 b 2 = 1 , a > b. Let E2 be another ellipse such that it touches the end points of major axis of E1 and the foci of E2 are the end points of minor axis of E1. If E1 and E2 have same eccentricities, then its value is:

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Let E₁ : $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,$ a > b. Let E₂ be another ellipse such that it touches the end points of major axis of E₁ and the foci of E₂ are the end points of minor axis of E₁. If E₁ and E₂ have same eccentricities, then its value is: