MHT CET · Maths · Pair of Lines
If the equation given by \(h x y+10 x+6 y+4=0\) represents a pair of lines, then \(h\) is equal to
- A 15
- B 30
- C 5
- D 10
Answer & Solution
Correct Answer
(A) 15
Step-by-step Solution
Detailed explanation
Here, \(a=0, b=0, h=\frac{h}{2}, g=5, f=3\) and \(c=4\) It represent a pair of lines
\(\therefore \left|\begin{array}{ccc}0 & h / 2 & 5 \\ h / 2 & 0 & 3 \\ 5 & 3 & 4\end{array}\right|=0\)
\(\Rightarrow 0-\frac{h}{2}\left[4 \frac{h}{2}-15\right]+5\left[\frac{3 h}{2}-0\right]=0\)
\(\Rightarrow -h^{2}+\frac{h 15}{2}+\frac{15 h}{2}=0\)
\(\Rightarrow -h^{2}+15 h =0 \)
\( \Rightarrow h(-h+15) =0 \)
\( \Rightarrow h =0,15\)
\(\therefore \left|\begin{array}{ccc}0 & h / 2 & 5 \\ h / 2 & 0 & 3 \\ 5 & 3 & 4\end{array}\right|=0\)
\(\Rightarrow 0-\frac{h}{2}\left[4 \frac{h}{2}-15\right]+5\left[\frac{3 h}{2}-0\right]=0\)
\(\Rightarrow -h^{2}+\frac{h 15}{2}+\frac{15 h}{2}=0\)
\(\Rightarrow -h^{2}+15 h =0 \)
\( \Rightarrow h(-h+15) =0 \)
\( \Rightarrow h =0,15\)
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