Q. If the line $ax + by + c = 0\ is\$a tangent to the curve $xy = 4,$ then
A) $a < 0,b > 0$
B) $a \leq 0,b > 0$
C) $a < 0,b < 0$
D) $a \leq 0,b < 0$
Explanation
(c)
Given curve is $xy = 4$
$\Rightarrow \ \ y = \frac{4}{x}$
$\therefore\ \ \frac{dy}{dx} = - \frac{4}{x^{2}}$
$\Rightarrow - \frac{4}{x^{2}} = - \frac{a}{b}$
$\Rightarrow \ \ x^{2} = \frac{4b}{a} > 0$
Which is true when
$a > 0,b > 0\ \ or\ \ a < 0,b < 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.