Question

If the line $\alpha x+by+c=0$ is a tangent to the curve $xy=4$, then

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

Answer 1

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

Slope of line $ax+by+c=0$ is
$\Rightarrow -\frac{a}{b}$
$y=\frac{4}{x}=1,\frac{dy}{dx}=-\frac{4}{x^2}$,
$-\frac{a}{b}=-\frac{4}{x^2}\Rightarrow \frac{a}{b}=\frac{4}{x^2}>0$
$a<0,b<0$