Question

If slopes of lines represented by kx² - 4xy + y² = 0 differ by 2, then k = ______ 

पर्याय

• 2

• 3

• 6

• 8

Answer 1

If slopes of lines represented by kx² - 4xy + y² = 0 differ by 2, then k = 3 

Explanation:

Given equation of lines is

kx² - 4xy + y² = 0 

∴ a = k, b = 1, h = -2

∴ `m_1 + m_2 = (-2h)/b = 4`

`m_1 m_2 = a/b = k`

According to the given condition,

m₁ - m₂ = 2

Now, (m₁ - m₂)² = (m₁ + m₂)² - 4m₁m₂

⇒ 2² = 4² - 4k ⇒ 4k = 12

⇒ k = 3