The lengths of the perpendiculars from the points m 2 , 2 m , m n , m + n and n 2 , 2 n to the line x + 3 y + 3 = 0 are in

Question

The lengths of the perpendiculars from the points m 2 , 2 m , m n , m + n and n 2 , 2 n to the line x + 3 y + 3 = 0 are in, Arithmetic progression, Geometric progression, Harmonic progression, None of these

MARKS App · Accepted Answer

The given line is x + 3 y + 3 = 0 … 1 Let p 1 , p 2 and p 3 are the lengths of the perpendiculars from the points A m 2 , 2 m , B m n , m + n and C n 2 , 2 n respectively on the given line, then p 1 = m 2 + 3 2 m + 3 1 + 3 ⇒ m + 3 2 2 p 2 = m n + 3 m + n + 3 1 + 3 ⇒ m + 3 n + 3 2 p 3 = n 2 + 3 2 n + 3 1 + 3 ⇒ n + 3 2 2 Clearly, p 1 . p 3 = p 2 2 ∴ p 1 , p 2 , p 3 are in GP

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