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Question

Tangents are drawn to the ellipse x216+y27=1 at the end points of the latus rectum. The area of quadrilateral formed by these tangents is

A
643 sq. units
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B
1283 sq. units
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C
2563 sq. units
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D
323 sq. units
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Solution

The correct option is B 1283 sq. units
For ellipse x216+y27=1,
e=1716=34

One end of latus rectum is
(ae,b2a)(3,74)
Therefore, equation of tangents at this point is

3x16+74.y7=1
3x16+y4=1
It meets the coordinate axes at (163,0) and (0,4).
Hence, the required area of quadrilateral
=4×area of AOB
=4×(12×163×4)=1283 sq. units

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