If the sum of the slopes of the lines represented by `x^(2) + kxy - 3y^(2) = 0` is twice their product, thent the vlaue of 'k' is

Options

A. 2
B. 1
C. `-1`
D. `-2`

Answer

D

Explanation

Given equation of lines is `x^(2)+kxy-3y^(2)=0` on comparing with `ax^(2)+2hxy+by^(2)=0`, we get a `=1,2h=k,b=-3`
Let `m_(1)` be the slopes of lines.
`:.m_(1)+m_(2)=-(2h)/(b)=(-k)/(-3)=(k)/(3)andm_(1)m_(2)=(a)/(b)=(-1)/(3)`
From the given condition, `m_(1)+m_(2)=2m_(1)m_(2)`
`:.(K)/(3)=(-2)/(3)`
`impliesK=-2`