Question

If the line $ax+by+c=0$ is a normal to the hyperbola $xy=1$, then

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

Answer 1

The correct option is A $a>0,b<0$

slope of normal $=t^2=-\frac{a}{b}$

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

$\therefore a>0,b<0$ and $a<0,b>0$.

Hence, option A.