Question

If the slope of one of the lines represented by kx² – 4xy + y² = 0 is thrice the other, then k is equal to ______.

Options

• 1

• 2

• 3

• 4

Answer 1

If the slope of one of the lines represented by kx² – 4xy + y² = 0 is thrice the other, then k is equal to 3.

Explanation:

Given equation of pair of lines is

kx² – 4xy + y² = 0 

∴ A = k, H = –2, B = 1

According to the given condition,

m₁ = 3m₂ 

m₁ + m₂ = `(2(-2))/1` = 4

⇒ 3m₂ + m₂ = 4

⇒ m₂ = 1

⇒ m₁ = 3

Now m₁m₂ = `"k"/1` = k

⇒ k = (3)(1) = 3