The centre of the sphere lies on the plane
Direction: Consider the following for the two (02) items that follow :<br>Let 2x^{2}+2y^{2}+2z^{2}+3x+3y+3z-6=0 be a sphere.
- A. 2x+2y+2z-3=0
- B. 4x+4y+4z-3=0
- C. 4x+8y+8z-15=0
- D. 4x+8y+8z+15=0 ✓
Correct Answer: D. 4x+8y+8z+15=0
Explanation
The center of the sphere is (-\frac{3}{4}, -\frac{3}{4}, -\frac{3}{4}). We substitute this point into the given plane equations. Testing the fourth option: 4(-\frac{3}{4}) + 8(-\frac{3}{4}) + 8(-\frac{3}{4}) + 15 = -3 - 6 - 6 + 15 = -15 + 15 = 0. Since it satisfies the equation, the center lies on the plane 4x+8y+8z+15=0.
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