Question:
The radius of the sphere $x^2 + y^2 + z^2 = 12x + 4y + 3z$ is
The radius of the sphere $x^2 + y^2 + z^2 = 12x + 4y + 3z$ is
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For sphere $x^2+y^2+z^2+2ux+2vy+2wz+d=0$, radius is $\sqrt{u^2+v^2+w^2-d}$.
Updated On: Apr 10, 2026
- $\frac{13}{2}$
- 13
- 26
- 52
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The Correct Option is A
Solution and Explanation
Step 1: Standard Form
Rewrite the equation as $x^2 + y^2 + z^2 - 12x - 4y - 3z = 0$. Here $u = -6, v = -2, w = -3/2$ and $d = 0$.
Step 2: Calculate Radius
Radius $R = \sqrt{u^2 + v^2 + w^2 - d}$. $R = \sqrt{(-6)^2 + (-2)^2 + (-3/2)^2 - 0}$. $R = \sqrt{36 + 4 + 9/4} = \sqrt{40 + 9/4} = \sqrt{169/4}$.
Step 3: Conclusion
$R = 13/2$.
Final Answer: (a)
Rewrite the equation as $x^2 + y^2 + z^2 - 12x - 4y - 3z = 0$. Here $u = -6, v = -2, w = -3/2$ and $d = 0$.
Step 2: Calculate Radius
Radius $R = \sqrt{u^2 + v^2 + w^2 - d}$. $R = \sqrt{(-6)^2 + (-2)^2 + (-3/2)^2 - 0}$. $R = \sqrt{36 + 4 + 9/4} = \sqrt{40 + 9/4} = \sqrt{169/4}$.
Step 3: Conclusion
$R = 13/2$.
Final Answer: (a)
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