Question

If the line $ax+by+c=0$ is normal to the curve $xy=2$, then

• A. $a>0,b>0$
• B. $a<0,b<0$
• C. $a>0,b<0ora<0,b>0$
• D. None of these

Answer 1

The correct option is C $a>0,b<0ora<0,b>0$

Given $xy=2\Rightarrow y=\frac{2}{x}$

$\Rightarrow \frac{dy}{dx}=-\frac{2}{x^2}$ ............ slope of tangent

Thus, slope of normal $=\frac{x^2}{2}$ (which is always positive) and it is given

$ax+by+c=0$ is normal whose slope $=\frac{-a}{b}$.

$\Rightarrow -\frac{a}{b}>0$ or $\frac{a}{b}<0$

$\therefore a$ and $b$ are of opposite sign.

Hence if $a>0,b<0$ or $a<0,b>0$