Question

If $a,b,c$ 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 is

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

Answer 1

The correct option is C $(1,-2)$

Given $a,b,c$ are in H.P, then
$b=\frac{2ac}{a+c}$ ....(i)
Substituting the value of $b$ in eq (i), we get
$c(2x+y)+a(y+2)=0$, which gives $y=-2$ and $2x+y=0$
Solving the obtained equations , we get
$x=1$ and $y=-2$
Therefore, the given line will pass through fixed point $(1,-2)$
Hence, the correct option is 'C'.