Question

If the line $ax+by+c=0$ is a normal to curve $xy+5=0,$ then $a$ and $b$ have

• A. Same sign
• B. Opposite sign
• C. Can't be discussed
• D. None of these

Answer 1

The correct option is A Same sign

$y=-\frac{5}{x}$
$\frac{dy}{dx}=\frac{5}{x^2}$
$\therefore$ Slope of normal $=-\frac{x^2}{5}<0;$ Hence, slope of normal will be negative.
Given The line $ax+by+c=0$
$\Rightarrow$ Slope $\frac{-a}{b}$ is negative $\Rightarrow a>0,b>0$ or $a<0,b<0$