Question

Find k, if one of the lines given by 6x² + kxy + y² = 0 is 2x + y = 0

Answer 1

Let m₁ be the slope of 2x + y = 0.

∴ m₁=-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.