If two distinct tangents can be drawn from the Point `(alpha,2)` on different branches of the hyperbola `x^2/9-y^2/(16)=1` then (1) `|alpha| lt 3/2` (2) `|alpha| gt 2/3` (3)`|alpha| gt 3` (4) `alpha =1`

Options

A. `|alpha|lt3//2`
B. `|alpha|gt2//3`
C. `|alpha|gt3`
D. none of these

Answer

A

Explanation

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)`