Circles
Two circles given by x^2 + y^2 = 9 and x^2 + y^2 - 6x + 5 = 0 intersect; what is the equation of their common chord, the radical axis?
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About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- circles
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
6x=14
The radical axis, which coincides with the common chord of two intersecting circles, is obtained simply by subtracting the two circle equations written in general form. Circle one is x^2 + y^2 - 9 = 0 and circle two is x^2 + y^2 - 6x + 5 = 0. Subtracting the second from the first eliminates the quadratic terms: (-9) - (-6x + 5) = 0, i.e. -9 + 6x - 5 = 0, giving 6x - 14 = 0, or 6x = 14. Option 6x = 4 results from adding rather than subtracting the constants. Option 6x = 9 averages the two constants instead of combining them correctly. Option x = 3 mistakes the radical axis for a circle boundary. This is the canonical JEE Advanced radical-axis method. Plausibility check: x = 14/6 ≈ 2.33 lies inside the first circle of radius 3, so a real common chord exists, confirming the result is geometrically valid.
This medium difficulty mathematics question is from the chapter coordinate geometry, covering the topic of circles. It appeared in the 2025 exam.
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