Question

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

• A. $1,2$
• B. $1,-2$
• C. $-1,2$
• D. $-1,-2$

Answer 1

Answer: (B)

$1,-2$

$a+b+1=0$
${xy}^{\prime }+y+a+{by}^{\prime }=0$
$y^{\prime }=\frac{-(y+a)}{(x+b)}$
$-\frac{(a+1)}{(1+b)}=2$
$2+2b+a+1=0$
$2+2b-b=0$
$b=-2$
$a=1$