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NDA 2022 Maths · Mathematics · Three Dimensional Geometry · hard

The equation of the sphere with centre (1,-2,2) passing through the origin is

Single correct option

The equation of the sphere with centre (1,−2,2)(1,-2,2) passing through the origin is
  1. A. x2+y2+z2+2x−4y+4z=0x^2+y^2+z^2+2x-4y+4z=0
  2. B. x2+y2+z2−2x+4y−4z=0x^2+y^2+z^2-2x+4y-4z=0
  3. C. x2+y2+z2−2x+4y−4z=9x^2+y^2+z^2-2x+4y-4z=9
  4. D. x2+y2+z2−2x+4y−4z+9=0x^2+y^2+z^2-2x+4y-4z+9=0
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Answer: (B) x2+y2+z2−2x+4y−4z=0x^2+y^2+z^2-2x+4y-4z=0

Radius2=1+4+4=9^2=1+4+4=9. Sphere: (x−1)2+(y+2)2+(z−2)2=9(x-1)^2+(y+2)^2+(z-2)^2=9, which expands to x2+y2+z2−2x+4y−4z+9=9x^2+y^2+z^2-2x+4y-4z+9=9, i.e. x2+y2+z2−2x+4y−4z=0x^2+y^2+z^2-2x+4y-4z=0. It has no constant term since it passes through the origin.
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