Question:
Which point could lie on the circle with radius 5 and center \( (1, 2) \)?
Which point could lie on the circle with radius 5 and center \( (1, 2) \)?
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For circle problems, always apply the equation \((x-h)^2 + (y-k)^2 = r^2\).
Updated On: Oct 3, 2025
- \( (4, 6) \)
- \( (3, 4) \)
- \( (3, -2) \)
- \( (-3, 6) \)
- \( (4, -1) \)
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The Correct Option is A
Solution and Explanation
Step 1: Use the equation of a circle.
A point \((x, y)\) lies on the circle with center \((h, k)\) and radius \(r\) if: \[ (x-h)^2 + (y-k)^2 = r^2 \] Step 2: Substitute values.
Here, \(h=1, k=2, r=5\). Check \((4, 6)\): \[ (4-1)^2 + (6-2)^2 = 3^2 + 4^2 = 9 + 16 = 25 = 5^2 \] So \((4, 6)\) lies on the circle.
Final Answer: \[ \boxed{(4, 6)} \]
A point \((x, y)\) lies on the circle with center \((h, k)\) and radius \(r\) if: \[ (x-h)^2 + (y-k)^2 = r^2 \] Step 2: Substitute values.
Here, \(h=1, k=2, r=5\). Check \((4, 6)\): \[ (4-1)^2 + (6-2)^2 = 3^2 + 4^2 = 9 + 16 = 25 = 5^2 \] So \((4, 6)\) lies on the circle.
Final Answer: \[ \boxed{(4, 6)} \]
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