Coordinate Geometry
Circles, Chord Length
jee_main_2026_jan_22_shift_1
Grade None
Question:
The circle \(x^2 + y^2 - 6x - 8y + 9 = 0\) intersects the y-axis at points A and B. Find AB.
A. 2√3
B. 2√5
C. 2√7
D. 6
Step-by-Step Solution
Key Concept: Put x=0, solve quadratic, find distance between roots.
Step 1: Put x=0: y² - 8y + 9 = 0. Step 2: y = [8 ± √(64-36)]/2 = [8 ± √28]/2 = 4 ± √7. Step 3: AB = |(4+√7) - (4-√7)| = 2√7.
Correct Answer: C
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