circles

Question

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

RankGuru · Accepted Answer

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

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