MHT CET · Maths · Pair of Lines
If one of the lines given by the equation \(x^{2}+k x y+2 y^{2}=0\) is \(x+2 y=0\), then \(\mathrm{k}=\)
- A 2
- B 1
- C 3
- D 4
Answer & Solution
Correct Answer
(C) 3
Step-by-step Solution
Detailed explanation
We have \(x^{2}+k x y+2 y^{2}=0\) i.e. \(1+k\left(\frac{y}{x}\right)+2\left(\frac{y}{x}\right)^{2}=0\)
Slope of line \(x+2 y=0\) is \(-\frac{1}{2}\)
Substituting \(\frac{y}{x}=-\frac{1}{2}\), we get
\(1+\mathrm{k}\left(-\frac{1}{2}\right)+2\left(-\frac{1}{2}\right)^{2}=0 \Rightarrow 1-\frac{\mathrm{k}}{2}+\frac{1}{2}=0 \Rightarrow \mathrm{k}=3\)
Slope of line \(x+2 y=0\) is \(-\frac{1}{2}\)
Substituting \(\frac{y}{x}=-\frac{1}{2}\), we get
\(1+\mathrm{k}\left(-\frac{1}{2}\right)+2\left(-\frac{1}{2}\right)^{2}=0 \Rightarrow 1-\frac{\mathrm{k}}{2}+\frac{1}{2}=0 \Rightarrow \mathrm{k}=3\)
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