Question:
The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is
The centres of a set of circles, each of radius 3, lie on the circle \( x^2 + y^2 = 25 \). The locus of any point in the set is
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The locus of points forming the centre of a set of circles can be determined by the equation of the circle they lie on.
Updated On: Jan 6, 2026
- \( x^2 + y^2 = 25 \)
- \( x^2 + y^2 = 3 \)
- \( x^2 + y^2 = 6 \)
- None of these
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The Correct Option is A
Solution and Explanation
Step 1: Analyzing the problem.
The centres of the circles lie on the given circle \( x^2 + y^2 = 25 \). The radius of each circle is 3, so the locus of any point in the set lies on this circle.
Step 2: Conclusion.
The locus of the points is \( x^2 + y^2 = 25 \), corresponding to option (1).
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