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Question

Let S and S be foci of an ellipse and B be any one of the extremities of its minor axis. If ΔSBS is a right angled triangle with right angle at B and area of SBS=8 sq. units, then the length of a latus rectum of the ellipse (in units) is :

A
2
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B
22
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C
42
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D
4
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Solution

The correct option is D 4
Let equation of ellipse be x2a2+y2b2=1, a>b
where S(ae,0), S(ae,0) and B(0,b)

ΔSBS is a right angled triangle with right angle at B
(SB)2+(SB)2=(SS)2a2e2+b2+a2e2+b2=4a2e2b2=a2e2e2=b2a21b2a2=b2a2a2=2b2a=2b

Given, area of (SBS)=8 sq. units
12×2ae×b=82b×b2 b×b=8b2=8b=22a=4
​​​​​​​
So, length of latus rectum
​​​​​​​=2b2a=2(8)4=4 units

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