Question

The slope of the tangent to the curve $xy+ax-by=0$ at the point $(1,1)$ is $2$ then values of $a$ and $b$ are respectively -

• A. $1,2$
• B. $2,1$
• C. $3,5$
• D. None of these

Answer 1

Answer: (A)

$1,2$

Given curve is $xy+ax-by=0$
Slope of tangent at $(1,1)$ is $x.\frac{dy}{dx}+y+a-b.\frac{dy}{dx}=0$
${\left(\frac{dy}{dx}\right)}_{(1,1)}=-{\left[\frac{(a+y)}{x-b}\right]}_{(1,1)}=-\frac{(a+1)}{1-b}$
$\therefore -\frac{(a+1)}{1-b}=2$
So, $2b-a=3$ ..........(1)
$\because (1,1)$ lies on curve $xy+ax-by=0$
$\therefore a-b=-1$ .........(2)
From (1) and (2), we get
$a=1,b=2$
Hence, option 'A' is correct.