Question

If the equation $kxy+10x+6y+4=0$ represents a pair of lines then value of k is

• A. $0$
• B. $15$
• C. $-15$
• D. $\frac{1}{15}$

Answer 1

Answer: (B)

$15$

The equation $S=A{x}^2+2Hxy+B{y}^2+2Gx+2Fy+C=0$ represents a pair of straight lines if the following conditions hold :

$\Delta =ABC+2FGH-A{F}^2-B{G}^2-C{H}^2=0$

$H^2\ge AB,G^2\ge AC,F^2\ge BC$

Here,

$A=0,B=0,C=4,F=3,G=5,H=\frac{k}{2}$

$\Delta =0+15k-0-0-k^2=0$

$\Rightarrow 15k-k^2=0$

$\Rightarrow k=0$ or $k=15$

But if $k$ is $0$, we only get a single line and not a pair of lines.

So, $k=15$