Question:
A circle passes through the points \((2, 3)\) and \((4, 5)\). If its centre lies on the line, \(y - 4x + 3 = 0\), then its radius is equal to :
A circle passes through the points \((2, 3)\) and \((4, 5)\). If its centre lies on the line, \(y - 4x + 3 = 0\), then its radius is equal to :
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The centre lies on the perpendicular bisector of the chord joining the two points, and on the given line.
Updated On: Nov 11, 2026
- \(2\)
- \(\sqrt5\)
- \(\sqrt2\)
- \(1\)
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The Correct Option is A
Solution and Explanation
The midpoint of (2, 3) and (4, 5) is (3, 4) and the chord has slope 1, so its perpendicular bisector is \(y - 4 = -(x - 3)\), i.e. \(x + y = 7\).
The centre is the intersection with \(y = 4x - 3\): \(x + 4x - 3 = 7 \Rightarrow x = 2,\ y = 5\).
Radius = distance from (2, 5) to (2, 3) = 2.
Answer: (1) \(2\)
The centre is the intersection with \(y = 4x - 3\): \(x + 4x - 3 = 7 \Rightarrow x = 2,\ y = 5\).
Radius = distance from (2, 5) to (2, 3) = 2.
Answer: (1) \(2\)
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