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`
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.
`thereforem_(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)`
`implies(1)^(2)=(-5)^(2)-4k` [given, `m_(1)-m_(2)=1" or "m_(2)-m_(1)=1`]
`implies1=25-4k`
`implies4k=24impliesk=6`