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The slopes of lines represented by x^2+2...

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

A

`+- (1)/(2)`

B

`+-(3)/(2)`

C

`+-1`

D

`+-3`

Text Solution

Verified by Experts

The correct Answer is:
B
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`.
`therefore m_1:m_2=1:2`
Let `m_1=m and m_2=2m`
`therefore m_1+m_2=-(2h)/(2)`
`rArr m+2m=-hrArr h=-3m`........(i)
and `m_1m_2=(a)/(b)`
`rArr m.2m=(1)/(2)rArr m=+-(1)/(2)` .........(ii)
From Eqs. (i) and (ii) , we get , `h=+-(3)/(2)`.
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