Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If ( α , β ) is a point on the circle whose centre is on the x-axis and which touches the line x + y = 0 at (2, –2), then find the greatest integral value of ‘ α ’.
Text Solution
Verified by ExpertsThe correct answer is:
6
(6) Equation of circle (x – 2) 2 + (y + 2) 2 + λ (x + y) = 0 ........(i)
Centre lies on the x-axis
∴ λ = – 4 put in (i)
∴ equation of circle is x 2 + y 2 – 8x + 8 = 0
( α , β ) lies on it ⇒ β 2 = – α 2 + 8 α – 8 ≥ 0
∴ greatest value of ‘ α ’ is 4 + 2 
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