Question

If $l,m,n$ are in arithmetic progression, then the straight line $lx+my+n=0$ will always pass through which of the following point?

• A. $(-1,2)$
• B. $(1,-2)$
• C. $(1,2)$
• D. $(2,1)$

Answer 1

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

The equation of given line is $lx+my+n=0$ ....$\left(1\right)$

If $l,m,n$ are in arithmetic progression then, $2m=l+n$ ...$\left(2\right)$

Equation $\left(2\right)$ can be written as, $l-2m+n=0$ ...$\left(3\right)$

Now comparing the equation $\left(3\right)$ with equation $\left(1\right)$, we can clearly see that line $lx+my+n=0$ passes through the point $(1,-2)$

Hence the correct option is $B$.