Q. If non-zero numbers $a,\ b,\ c$ are in HP, then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0\$always passes through a fixed point. That point is
A) $\left( 1,\ - \frac{1}{2} \right)$
B) $(1,\ - 2)$
C) $( - 1,\ - 2)$
D) $( - 1,\ 2)$
Explanation
(b)
Since, $a,b,c$ are in HP
$\therefore\ \frac{2}{b} = \frac{1}{a} + \frac{1}{c}\ \Rightarrow \ \frac{1}{a} - \frac{2}{b} + \frac{1}{c} = 0$
So, straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point $(1,\ - 2)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.