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CGP EDU Academic Team
Published on: August 14, 2026
Find the greatest integer values of a for which the point (2a, a + 1) is an interior point of the larger segment of the circle x 2 + y 2 − 2x − 2y − 8 = 0 made by the chord whose equation is x − y + 1 = 0.
Text Solution
Verified by ExpertsThe correct answer is:
1
(1)Point (2a, a + 1) lies inside circle x 2 + y 2 – 2x – 2y – 8 = 0
4a 2 + (a + 1) 2 – 2(2a) – 2(a + 1) – 8 < 0 ⇒ 5a 2 – 4a – 9 < 0
5a 2 – 9a + 5a – 9 < 0 ⇒ a(5a – 9) + 1(5a – 9) < 0
(5a – 9) (a + 1) < 0 ⇒ a ∈ (–1, 9/5)
centre & (2a, a + 1) lies on same side w.r.t. line x – y + 1 = 0
2a – (a + 1) + 1 > 0 ⇒ a > 0
Hence a ∈ (0, 9/5)
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