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The directrix of an ellipse with eccentricity  \mathrm {\frac{1}{\sqrt{2}}} is   \mathrm {\: \: \: \: x+y=1}  If the corresponding focus is  (1,2) , then the length of the minor axis is
 

Option: 1

\sqrt{2}


Option: 2

2


Option: 3

2 \sqrt{2}


Option: 4

4


Answers (1)

best_answer

The distance of  \mathrm S(1,2)  from the directrix

\begin{aligned} &\mathrm { x+y=1 \text { is } \frac{1+2-1}{\sqrt{2}}=\sqrt{2} }\\ & \mathrm {\therefore \quad \frac{a}{e}-a e=\sqrt{2} \Rightarrow \sqrt{2} a-\frac{a}{\sqrt{2}}=\sqrt{2} \Rightarrow a=2} \\ &\mathrm { 2 b=2 a \sqrt{1-e^2}=4 \sqrt{1-\frac{1}{2}}=2 \sqrt{2}} . \end{aligned}

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SANGALDEEP SINGH

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