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If (sqrt(3))b x+a y=2a b touches the ell...

If `(sqrt(3))b x+a y=2a b` touches the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1` , then the eccentric angle of the point of contact is (a)`pi/6` (b) `pi/4` (c) `pi/3` (d) `pi/2`

A

`pi//6`

B

`pi//4`

C

`pi//3`

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
A
The equation of tanents is
`(x)/(a)(sqrt(3))/(2)+(y)/(b)(1)/(2)=1" "(1)`
and the equation of tangent at the point `(a cos phi, b sin b phi)` is `(x)/(a)cos phi+(y)/(b) sin phi=1 " "(2)`
Comparing (1) and (2), we have
`cos phi =(sqrt(3))/(2) and sin phi=(1)/(2)`
Hence, `phi=pi//6`
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