Question

If the slope of the curve $y=\frac{ax}{b-x}$ at the point (1, 1) is 2 then values of a and b respectively

• A. 1, -2
• B. -1, 2
• C. 1, 2
• D. None of these

Answer 1

The correct option is C

1, 2

We have, $y=\frac{ax}{b-x}$
$\Rightarrow =\frac{dy}{dx}=\frac{(b-x)a-ax(-1)}{(b-x^2)}=\frac{ab}{(b-x{)}^2}$
$\therefore {\left[\frac{dy}{dx}\right]}_{(1,1)}=\frac{ab}{(b-1{)}^2}$(given)....(1)
Since the curve passes through the point (1,1), therefore,
$1=\frac{a}{b-1}\Rightarrow a=b-1$
On putting a=b-1 in equation (1), we get
$\frac{(b-1)b}{(b-1{)}^2}=2\Rightarrow b=2.\therefore 1=2-1=1.$
Hence a =1, b=2
Hence (c) is the correct answer.