Consider a straight line `x/a + y/b =1` , such that it cuts the asymptotes of hyperbola `xy = 1` in points A and B and the hyperbola itself in P and Q, then`(AP )/ (BQ) =lamda` lambda where `2lambda + 1` is

Answer

3

Explanation

`A(a,0), B(0,b)`
Put `y=1/x`
`x^(2)-ax+a/b=0` and `x=1/y`
`y^(2)-by+b/a=0`
`AP^(2)=(x_(1)-a)^(2)+y_(1)^(2)=(a-x_(2)-a)^(2)+(b-h_(2))^(2)=x_(2)^(2)+(b-y_(2)^(2))=BQ^(2)`