If p is the lengt

Given equation is

Since, p is the length of perpendicular drawn from the origin to the given line

Squaring both the sides, we have

…(i)

Since, a², b² and p² are in AP

∴ 2p² = a² + b²

…(ii)

Form eq. (i) and (ii), we get

⇒ (a² + b²)(a² + b²) = 2(a²b²)

⇒ a⁴ + b⁴ + a²b² + a²b² = 2a²b²

⇒ a⁴ + b⁴ = 0

Hence Proved