Question

If the equation given by $hxy+10x+6y+4=0$ represents a pair of lines, then $h$ is equal to

• A. $15$
• B. $30$
• C. $5$
• D. $10$

Answer 1

The correct option is A $15$

Here, $a=0,b=0,h=\frac{h}{2},g=5,f=3$ and $c=4$
It represent apair of lines
$\therefore \left|\begin{array}{ccc}0& h/2& 5\\ h/2& 0& 3\\ 5& 3& 4\end{array}\right|=0$
$\Rightarrow 0-\frac{h}{2}\left[4\frac{h}{2}-15\right]+5\left[\frac{3h}{3}-0\right]=0$
$\Rightarrow -h^2+\frac{h15}{2}+\frac{15h}{2}=0$
$\Rightarrow -h^2+15h=0$
$\Rightarrow h(-h+15)=0$
$\Rightarrow h=0,15$