If slopes of lines represented by `kx^(2)+5xy+y^(2)=0` differ by 1, then k=

Options

A. `2`
B. 3
C. 6
D. 8

Answer

C

Explanation

Given pair of lines be
`kx^(2) +5xy +y^(2) = 0"…."(i)`
On comparing Eq. (i) with
`ax^(2) + 2hx +by^(2) = 0`, we get
`a = k, b = 1` and `2h =5`
Let `m_(1)` and `m_(2)` be two slopes of pair of lines.
`:. m_(1) + m_(2) = (-2h)/(b) = -5`
and `m_(1)m_(2) = (a)/(b) = k`
Now, `(m_(1) - m_(2))^(2) = (m_(1) + m_(2))^(2) - 4m_(1)m_(2)`
`rArr (1)^(2) = (-5)^(2) - 4 k`
[given, `m_(1) - m_(2) = 1` or `m_(2) - m_(1) = 1` ]
`rArr 1 = 25 - 4k`
`rArr 4k = 24 rArr k = 6`