#### Question

Find k, if one of the lines given by 6x^{2} + kxy + y^{2} = 0 is 2x + y = 0

#### Solution

Let m_{1} be the slope of 2x + y = 0.

∴ m_{1}=-2

`6x^2+kxy+y^=0`

`therefore a=6,h=k/2,b=1`

`m_1+m_2=-(2h)/b=-k`

`-2+m_2=-k`

`m_2=-k+2`

`Now, m_1m_2 =a/b`

`(-2)(-k+2)=6`

`2k-4=6`

`2k=10`

`k=10/2`

`k=5`

The value of k is 5.

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#### APPEARS IN

Solution Find k, if one of the lines given by 6x2 + kxy + y2 = 0 is 2x + y = 0 Concept: Pair of Straight Lines - Pair of Lines Not Passing Through Origin-combined Equation of Any Two Lines.