If the line \(ax+by+c=0\) is a normal to the curve \(xy=4\), then

\(a<0,b<0\) \(a>0,b>0\) \(a>0,b<0\) \(a<0,b=0\)

\(a>0,b<0\)

\(y=-\frac{a}{b}x-\frac{c}{b}\) So, \(m=-\frac{a}{b}\hspace{6cm}\) Given \(xy=4\) So, \(\frac{dy}{dx}=-\frac{y}{x}\hspace{7cm}\) Slope of normal\(=\frac{x}{y}\hspace{8cm}\) Thus, \(\frac{x}{y}=-\frac{a}{b}\)