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Question

The slope of the diameter of the ellipse x2a2+y2b2=1, whose length is the GM of the major and minor axes, is:

A
ab
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B
ab
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C
ba
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D
ab
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Solution

The correct option is B ba
The length of the major axis is 2a and the length of minor axis is 2b

The diameter of ellipse is 2a×2b=2ab

So the point on ellipse will be in the form of

(abcosθ,absinθ)
If we substitute it in the ellipse equation , we get bacos2θ+absin2θ=1

cosθ=aa+b

So we get tanθ=ba

Therefore the correct option is C

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