tangents are drawn from ( a ,b ) to the hyperbola     making angles A and B with the transverse axis. if tanA tanB = 2 , then  is

give the answer in terms of a

hyp is x²/2 - y²/3 = 1

tangent to hyp, Ty=mx + root(a²m²-b²)

y=mx + root(2m²-3)

this passes through (a, b)

So, b=am + root(2m²-3)

or a²m² + b² - 2abm = 2m² - 3

solving, m1m2 = (b²+3)/(a²-2) = tanAtanB = 2

b²=2a² - 7