Question

If slopes of lines represented by kx² + 5xy + y² = 0 differ by 1, then k = ______.

विकल्प

• 2

• 3

• 6

• 8

Answer 1

If slopes of lines represented by kx² + 5xy + y² = 0 differ by 1, then k = 6.

Explanation:

We have, pair of lines

kx² + 5xy + y² = 0  ...(i)

After comparing equation (i) with

ax² + 2hx + by² = 0, we get

a = k, b = 1 and 2h = 5

Suppose m₁ and m₂ are two slopes of pair of lines.

Then m₁ + m₂ = `(-2h)/b` = –5 and m₁m₂ = `a/b` = k

As, (m₁ – m₂)² = (m₁ + m₂)² – 4m₁m₂

`\implies` (1)² = (–5)² – 4k

`\implies` 4k = 24

`\implies` k = 6