Question

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

• A. $a<0,b>0$
• B. $a>0,b<0$
• C. $a>0,b>0$
• D. $a<0,b<0$

Answer 1

Answer: (A), (B)

The correct options are
A $a<0,b>0$
B $a>0,b<0$

$x{y}^{\prime }+y=0$
Or
$y^{\prime }=\frac{-y}{x}$
Hence slope of normal
$=\frac{x}{y}$
$=\frac{2}{y^2}$
Hence the slope is always positive.
Now
slope of the line is $\frac{-a}{b}$
Hence we are left with 2 options.
Either
$a<0$ and $b>0$
Or
$a>0$ and $b<0$.