Q60 / 150 · MHT CET 2009 · Mathematics

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

  • Correct answer
    A
    15
  • B
    30
  • C
    5
  • D
    10

Solution

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

Hence, the correct answer is option: 'A'.

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