HyperbolaHardBloom L3
Question
Straight line $Ax + By + D = 0$ would be tangent to $xy = c^{2}$, if:
Options
A.$A > 0,B > 0$
B.$A < 0,B < 0$
C.$A > 0,B < 0$
D.$A < 0,B > 0$
Solution
Sol. $y = \frac{c^{2}}{x}$ is decreasing function
$$\begin{matrix} & \ \Rightarrow \text{~}\text{slope}\text{~} = - \frac{A}{B} < 0 \\ & \ \Rightarrow \frac{A}{B} > 0 \\ & \ \Rightarrow A > 0,B > 0\text{~}\text{or}\text{~}A < 0,B < 0 \end{matrix}$$
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