Question:
If the equation of the sphere through the circle $x^2 + y^2 + z^2 = 5$, $2x + 3y + 4z = 5$ and through the origin is $x^2 + y^2 + z^2 - 2x - 3y - 4z + C = 0$, then the value of $C$ is
If the equation of the sphere through the circle $x^2 + y^2 + z^2 = 5$, $2x + 3y + 4z = 5$ and through the origin is $x^2 + y^2 + z^2 - 2x - 3y - 4z + C = 0$, then the value of $C$ is
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Substitute known points directly to find constants quickly.
Updated On: Apr 30, 2026
- $1$
- $-1$
- $0$
- $5$
- $2$
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The Correct Option is C
Solution and Explanation
Concept:
A sphere must satisfy the coordinates of any point through which it passes.
Step 1: Given that sphere passes through origin \[ (0,0,0) \]
Step 2: Substitute in equation \[ 0 + 0 + 0 - 0 - 0 - 0 + C = 0 \] \[ C = 0 \]
Step 3: Conclusion \[ \boxed{0} \]
Step 1: Given that sphere passes through origin \[ (0,0,0) \]
Step 2: Substitute in equation \[ 0 + 0 + 0 - 0 - 0 - 0 + C = 0 \] \[ C = 0 \]
Step 3: Conclusion \[ \boxed{0} \]
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