Question

Find the values of $a$ and $b$ it the slope of the tangent to the curve $xy+ax+by=2$ at $(1,1)$ is $2$.

Answer 1

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

$\therefore$ & $\frac{dy}{dx}=2$

Now,

$2\times +1+a+2b=0$

$\Rightarrow 3+a+2b=0$

$\therefore a+2b=-3$ ---(1)

Given (1,1) so,

$1+a+b=2$

$a+b=1$ ---(2)

solve (1 ) & (2)

$a+2b=-3$ $a-4=1$

$a+b=2$ $a=5$

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____________

$b=-4$

$\therefore a=5,b=-4$