If the slope of the curve y=(a x)/(b-x) at the point (1, 1) is 2 , th…

We have,

$y=\frac{a x}{b-x}$ at point (1, 1)

$⇒1=\frac{a}{b-1}$ so $b-1=a$ so $b=a+1$  ...(1)

Slope = 2 at (1, 1)

so $yb-yx=ax$

differentiating ⇒ $y'(b-x)-y=a$ 

at (1, 1)

$⇒ 2'(b-1)-1=a$ 

$y'=2$

from (1) $b-1=a$

so $2a-1=a$

$⇒a=1$

so from (1) $b=2$