Question

Find the equation of the sphere through the four points (4,-1,2) (0,-2,3) (1,-5,-1) (2,0,1)​

Answer 1

Answer:

Solution :

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

So, Equation of sphere be: (x−a)2+(y−b)2+(z−c)2=r2

It passes through the points A(4.−1.2),B(0,−2,3),C(1,−5,−1)andD(2,0,1)

By point A, (4−a)2+(−1−b)2+(2−c)2=r2

By point B, (0−a)2+(−2−b)2+(3−c)2=r2

By point C, (1−a)2+(−5−b)2+(−1−c)2=r2

By point D, (2−a)2+(0−b)2+(1−c)2=r2

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

Step-by-step explanation:

I hope it is helpul for you