Question

If the area of the rhombus enclosed by the lines $lx\pm my\pm n=0$ be $2$ sq. units, then

• A. $l,m,n$ are in G.P.
• B. $l,n,m$ are in G.P.
• C. $lm=n$
• D. $ln=m$

Answer 1

Answer: (B)

$l,n,m$ are in G.P.

Intercept cut by lines on x-axis and y-axis are$|\frac{n}{m}|$and$|\frac{n}{l}|$respectively .
Area of rhombus is$=\frac{1}{2}\times diagona{l}_1\times diagona{l}_2=\frac{1}{2}\times \frac{2n}{m}\times \frac{2n}{l}=\frac{2n^2}{lm}=2$ $⟹n^2=lm$

thus $l,n$ and $m$ are in G.P.