Question

obtain the equation of the sphere through the four points​

Answer 1

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Equation of sphere

x2+y2+z2+2ux+2vy+2wz+d=0

It passes through

(3,0,0) 9+6u+d=0         .....(i)

(0,−1,0)  (1−2v+d=0         ....(ii)

(0,0,−2)  4−4w+d=0         ....(iii)

Also centre (−u,−v,−w) lies on the plane

3x+2y+4z=1

−3u−2v−4w=1         .....(iv)

By solving equations (i), (ii), (iii), and (iv)

We get u=−34

v=0

w=43

d=−1

then putting the values of u, v, w, d in the above equation

6(x2+y2+z2)−16x+9z−6=0.

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