Question

Find the equation of the sphere passing to the point (2,0,1)(1,-5,-1)(0,-2,3)(4,-1,2)

Answer 1

Answer:

Let the `center(a,b,c)` and `radius=r`

So, Equation of sphere be: `(x-a)^2+ (y-b)^2+ (z-c)^2=r^2`

It passes through the points `A(4.-1.2), B(0,-2,3), C(1,-5,-1) and D(2,0,1)`

By point A, `(4-a)^2+ (-1-b)^2+ (2-c)^2 =r^2`

By point B, `(0-a)^2+ (-2-b)^2 + (3-c)^2=r^2`

By point C, `(1-a)^2 + (-5-b)^2+ (-1-c)^2=r^2`

By point D, `(2-a)^2+ (0-b)^2+ (1-c)^2=r^2`

On solving We get, `a=2, b=-3, c=1, r=3`

Hence, Equation of sphere is= `(x-2)^2+ (y+3)^2 + (z-1)^2=9`