Question

The curve given by $x+y=e^{xy}$ has a tangent parallel to the y-axis at the point

• A. $(0,1)$
• B. $(1,0)$
• C. $(1,1)$
• D. $(-1,-1)$

Answer 1

The correct option is B $(1,0)$

Given curve is $x+y=e^{xy}$
On differentiating w.r.t $x$ we get
$1+\frac{dy}{dx}=e^{xy}\{y+x\frac{dy}{dx}\}$

$\Rightarrow \frac{dy}{dx}=\frac{y{e}^{xy}-1}{1-x{e}^{xy}}$

Since, tangent is parallel to y-axis
Here, $\frac{dy}{dx}=\infty \Rightarrow 1-x{e}^{xy}=0$
$\Rightarrow 1-x(x+y)=0$
This holds for $x=1,y=0$