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If two distinct tangents can be drawn from the point `(alpha, alpha+1)` on different branches of the hyperbola `(x^(2))/(9)-(y^(2))/(16)=1`, then find the values of `alpha`.

A

`|alpha|lt3//2`

B

`|alpha|gt2//3`

C

`|alpha|gt3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
For two distinct tangents on different branches, the point should lie on the line y = 2 and between A and B (where A and B are the points on the asymptotes).
The equations of asymptotes are
`4x=pm 3y`.
Solving with y = 2, we have
`x= pm(3)/(2)`
`therefore" "-(3)/(2)ltalpha lt(3)/(2)`
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