Question

Find k, if the slope of one of the lines given by kx² + 8xy + y² = 0 exceeds the slope of the other by 6.

Options

• 6

• 7

• -6

• -7

Answer 1

7

Explanation:

According to the given condition,

m₁ = m₂ + 6   ....(i)

Comparing kx² + 8xy + y² = 0 with

ax² + 2hxy + by² = 0, we get

a = k, 2h = 8, b = 1

Since, m₁ + m₂ = `(-2"h")/"b"` = - 8   ....(ii)

and m₁.m₂ = `"a"/"b"` = k    ...(iii)

∴ m₁ + 6 + m₂ = - 8    ....[From (i) and (ii)]

⇒ 2m₂ = - 14

⇒ m₂ = - 7

and (m₂ + 6)m₂ = k   ....[From (i) and (iii)]

∴ (- 7 + 6)(- 7) = k

⇒ k = 7