Let the equation of two ellipses E1:x23+y22=1 and E2:x216+y2b2=1. If the product of their eccentricities is 12, then the length of the minor axis of E2 is___

e1.e2=1213.16−b24=12⇒b=2Length of minor axis of E2=2b=4

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Let the equation of two ellipses $E_{1} : \frac{x^{2}}{3} + \frac{y^{2}}{2} = 1$ and $E_{2} : \frac{x^{2}}{16} + \frac{y^{2}}{b^{2}} = 1$ . If the product of their eccentricities is $\frac{1}{2}$ , then the length of the minor axis of E₂ is___

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$e_{1.} e_{2} = \frac{1}{2}$

$\frac{1}{\sqrt{3}} . \frac{\sqrt{16 - b^{2}}}{4} = \frac{1}{2} \Rightarrow b = 2$

Length of minor axis of E₂=2b=4

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