Question

If non-zero numbers $a,b,c$ are in H.P., then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ always passes through a fixed point. That point is :

• A. $(-1,2)$
• B. $(-1,-2)$
• C. $(1,-2)$
• D. $(1,-\frac{1}{2})$

Answer 1

Answer: (C)

$(1,-2)$

As $a,b,c$ are in H.P. $\Rightarrow \frac{2}{b}-\frac{1}{a}-\frac{1}{c}=0$
Comparing with $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$
$\Rightarrow \frac{x}{-1}=\frac{y}{2}=\frac{1}{-1}=0\Rightarrow x=1,y=-2$
Hence given line must pass through $(1,-2)$