If non-zero numbers $a, b, c$ are in H.P., then the straight line $\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$…
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
$(-1,2)$
$(-1,-2)$
$(1,-2)$
$\left(1,-\frac{1}{2}\right)$
Solution
a, b, c are in H.P.
$
\begin{aligned}
& \Rightarrow \frac{2}{b}-\frac{1}{a}-\frac{1}{c}=0 \\
& \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0 \\
& \Rightarrow \frac{x}{-1} \quad-\frac{1}{-1} \quad \therefore x=1, y=-2
\end{aligned}
$