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Question

The minimum area of triangle formed by the tangents to the ellipse x2a2+y2b2=1 and coordinate axes is:


A

ab sq. units

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B

(a+b)22 sq. units

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C

a2+b22 sq. units

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D

a2+ab+b23

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Solution

The correct option is A

ab sq. units


Equation of tangent to given ellipse is
y=mx+a2m2+b2
It meets axes at (a2m2+b2m,0) and (0,a2m2+b2)
Area of triangle
=12a2m2+b2m
=12a2m+b2mab
(Using the inequality arithmetic mean greater than or equal to geometric mean)
Hence A is the correct answer.


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