Find the equation of the sphere having centre (-1,2,-3) and the radius of 3 units.

Correct option is C

Given:
Centre o sphere =(-1,2,-3)
Radius = 3units
Formula Used:
Equation of sphere = $$(x-a)^2 +(x-b)^2+(x-c)^2 =r^2$$​​
Where a, b, c are co-ordinates and r is radius
Solution:
Centre is (-1,2,-3)
​$$(x-(-1))^2 +(y-(2))^2+(z-(-3))^2 =3^2 \\\ \\=(x+1)^2 +(y-(2))^2+(z+3)^2 =3^2 \\\ \\= x^2 +1^2 +2x +y^2 +2^2 -4y +z^2 +3^2+ 6z =9 \\\ \\= x^2 +1 +2x +y^2 +4 -4y +z^2 +9+ 6z =9 \\\ \\= x^2+y^2 +z^2 +2x -4y+ 6z +5 =0$$​​