Practicing Success
If the line ax + by + c = 0 is a tangent to the curve xy = 9, then |
(a), (b) (a), (d) (a), (c) (b), (d) |
(a), (d) |
We have $x y=9 \Rightarrow y=\frac{9}{x} \Rightarrow \frac{d y}{d x}=-\frac{9}{x^2}$ ........(i) Let $a x+b y+c=0$ be a tangent to the curve $x y=9$ at $\left(x_1, y_1\right)$ Then, $\left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)}$ = Slope of the line ax + by + c = 0 $\Rightarrow -\frac{9}{x_1^2}=\frac{-a}{b}$ $\Rightarrow \frac{x_1^2}{9}=\frac{b}{a}$ $\Rightarrow \frac{b}{a}>0$ ⇒ a and b are the same sign. ⇒ (a > 0 and b > 0) or, (a < 0 and b < 0) |