Answer: Both A and C are equivalent.
- A (x-1)<sup>2</sup>+(y+1)<sup>2</sup>+(z-2)<sup>2</sup>=6
- B x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>=6
- C x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>-2x+2y-4z=0
- D Both A and C are equivalent
Correct answer: D. Both A and C are equivalent
Explanation: Radius = sqrt(1+1+4) = sqrt(6). Equation A: (x-1)<sup>2</sup>+(y+1)<sup>2</sup>+(z-2)<sup>2</sup>=6. Expanding: x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>-2x+2y-4z+1+1+4=6, so x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>-2x+2y-4z=0 (equation C). Both A and C are equivalent.
Three mutually perpendicular axes x, y, z meeting at the origin O, with a point P located by its (x, y, z) coordinates.
Concept context
Lines and planes in 3D space, direction cosines, distances, and angles