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

Options

A. `x^2+y^2+z^2+4x-6y-8z=7`
B. `x^2=y^2+z^2+6x-4y-8z=7`
C. `x^2+y^2+z^2+4x-6y-8z=4`
D. `x^2+y^2+z^2+4x+6y+8z=4`

Answer

A

Explanation

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