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Maths Straight Line Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let 0 < p < q and a ≠ 0 such that the equation

px 2 + 4 λ xy + qy 2 + 4a (x + y + 1) = 0

represents a pair of straight lines, then a can lie in the interval

(– ∞ , ∞ )

(– ∞ , p]

[p, q]

[q, ∞ )

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b, d)

p.q.4a + 2.2a.2a.2 λ – p. 4a 2 – q.4a 2 – 4a.4 λ 2 = 0

⇒ 4 λ 2 – 4a λ + {(p + q) a – pq} = 0

( Θ a ≠ 0)

Θ λ ∈ R, 16a 2 – 4.4 {(p + q) a – pq} ≥ 0

or (a – p (a – q) ≥ 0

∴ a ≤ p or a ≥ q.

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