Question

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

Answer 1

Answer: (B)

$(1,-2)$

a,b,c are in H.P

$\therefore \frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in A.P

$\therefore \frac{2}{b}=\frac{1}{a}+\frac{1}{c}$ ________ (1)

$\therefore \frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0$ ________ (2)

$\therefore$ From (1)

$\frac{1}{a}+\frac{1}{c}-\frac{2}{b}=0$ ______ (3)

$\therefore$ From (2) & (3)

We infer that,

$(x=1,y=-2)$

$\therefore$ Point is $(1,-2)$