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If (x, y) lies on the circle with the segment joining (0, 1) and (2, 3) as a diameter, then x² + y² − 2x − 4y + 3 = 0. The two points where this circle crosses the y-axis have y coordinates:
Ay = 0 and y = 4
By = 1 and y = 3
Cy = 1 and y = 4
Dy = 0 and y = 3
Answer & Solution
Correct answer: B. y = 1 and y = 3
1. The y-axis corresponds to x = 0.
2. Substituting x = 0: y² − 4y + 3 = 0.
3. Factor: (y − 1)(y − 3) = 0.
4. So y = 1 or y = 3.
5. The circle therefore meets the y-axis at (0, 1) and (0, 3) — these are exactly the diameter endpoints, confirming the result.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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