Question

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

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

Answer 1

The correct option is A $1,2$

$xy+ax-by=0$

$(1,1)$ lies on curve

$1+a-b=0$

$a-b=-1$ ....... $\left(i\right)$

$y+x\frac{dy}{dx}+a-b\frac{dy}{dx}=0$

$1+2+a-2b=0$

$a-2b=-3$ ........ $\left(ii\right)$

Solving $\left(i\right)$ and $\left(ii\right)$, we get

$a=1,b=2$