Question

If a, b, c are in harmonic progression, then 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. $( 1 , - 1 / 2 )$

Answer 1

Answer: (C)

$( 1 , - 2 )$

Answer 2

a, b, c are in H. P., then $\frac { 2 } { b } = \frac { 1 } { a } + \frac { 1 } { c }$ .....(i)

Given line is $\frac { x } { a } + \frac { y } { b } + \frac { 1 } { c } = 0$ .....(ii)

Subtracting both $\frac { 1 } { a } ( x - 1 ) + \frac { 1 } { b } ( y + 2 ) = 0$

Since $a \neq 0 , b \neq 0$

So, $( x - 1 ) = 0 \Rightarrow x = 1$ and $( y + 2 ) = 0 \Rightarrow y = - 2$ .

Trick : Checking from options, let a, b, c are $\frac { 1 } { 1 } , \frac { 1 } { 2 } , \frac { 1 } { 3 }$ .

Then $x + 2 y + 3 = 0$will satisfy (3) option.