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If any tangent to the ellipse (x^(2))/(1...

If any tangent to the ellipse `(x^(2))/(16) + (y^(2))/(9) = 1` intercepts equal lengths l on the both axis, then l =

A

`3`

B

`5`

C

`sqrt(5)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
The equation of any tangent of the given ellipse is
`x/4 cos theta + y/3 sin theta = 1`
The tangent meet `x`-axis at `A ((4)/(cos theta) ,0)`
and `y`-axis at `B(0,(3)/(sintheta))`
Given `(4)/(costheta) = l` and `(3)/(sintheta) = l`
`rArr cos^(2)theta + sin^(2) theta = (16)/(l^(2)) + (9)/(l^(2)) rArr l = 5`
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