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NDA2018MathematicsThree Dimensional GeometryActual

What is the equation to the sphere whose centre is at (-2,3,4) and radius is 6 units?

Options

  1. Ax^2+y^2+z^2+4 x-6 y-8 z=7
  2. Bx^2+y^2+z^2+6 x-4 y-8 z=7
  3. Cx^2+y^2+z^2+4 x-6 y-8 z=4
  4. Dx^2+y^2+z^2+4 x+6 y+8 z=4

Correct answer

A. x^2+y^2+z^2+4 x-6 y-8 z=7

Step-by-step solution

Given, centre of sphere (h, k, l)=(-2,3,4) radius ( r )=6 units. Equation of sphere is (x-h)^2+(y-k)^2+(z- )^2=r^2 aligned & ( x +2)^2+( y -3)^2+( z -4)^2=6^2 & x ^2+4 x +4+ y ^2-6 y +9+ z ^2-8 z +16=36 & x ^2+ y ^2+ z ^2+4 x -6 y -8 z =7 aligned

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