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Question

If the line x2y=12 is tangent to the ellipse x2a2+y2b2=1 at the point (3,92), then the length of the latus rectum of ellipse is :

A
9
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B
83
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C
5
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D
122
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Solution

The correct option is A 9
x12y6=1 (1) is tangent to the ellipse x2a2+y2b2=1 at the point (3,92)

Equation of tangent to the ellipse at the point (3,92) is given by,
xx1a2+yy1b2=1
3xa29y2b2=1 (2)
On equating (1) and 2, we have
a23=12a2=36
2b29=62b2=54

Therefore, length of latus rectum =2b2a=9

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