Circles

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The radius of the circle x² + y² - 6x + 4y - 12 = 0 is

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Subject: mathematics
Chapter: coordinate geometry
Topic: circles
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

Identify General Form: The equation is $x^{2} + y^{2} + 2 gx + 2 f y + c = 0$ .
- Compare: $2 g = - 6 ⟹ g = - 3$
- Compare: $2 f = 4 ⟹ f = 2$
- Constant: $c = - 12$
Radius Formula: $r = g^{2} + f^{2} - c$ .
Calculation:
- $r = (- 3)^{2} + 2^{2} - (- 12)$
- $r = 9 + 4 + 12 = 25$
Conclusion: Radius $r = 5$ .

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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