Question

if the slope of the lines represented by 6x²+ 2hxy+ y² = 0 are in ratio 1: 2 then h = ?

Answer 1

6x² + 2 h x y + y² = 0
let the slopes be m1 and m2. Then from the equation,
m1 * m2 = 6
m1 + m2  = - 2 h
m2 = 2 m1  from given ratio
so 2 m1² = 6 => m1 = 2    m2 = 4
h = -1/2 (2+4) = -3

Answer 2

m1 =2
m2=4
h=-1by2(2+4)
=--3