The slopes of lines represented by `x^2+2hxy+2y^2=0` are in the ratio `1:2`, then h equals .

Options

A. `+- 1/2`
B. `+- 3/2 `
C. `+-1`
D. `+-3`

Answer

B

Explanation

On comparing the given equation with
`ax^(2)+ 2hxy + by^(2) =0`
We get
a=1 , 2h= 2h , and b =2
Let the slopes of lines are ` m_(1) and m_(2)`
` m_(1) : m_(2) = 1:2 `
Let ` m_(1) = m and m_(2) = 2m`
` m_(1) + m_(2) = -(2h)/2`
` Rightarrow m + 2m =-h`
` Rightarrow h = -3 m `
`and m_(1)m_(2) = a/b`
` Rightarrow m.2m = 1/2 Rightarrow 1/2 Rightarrow m = +- 1/2`
From Eqs. (i) and (ii) ,we get
` n = +- 3/2`