the plane x+2y+3z=6 meets the axis at A,B,C.Find the equation of the circumcircle of the triange ABC and its c

Question

plz tell me answer of this question....fast as possible...!

Answer 1

The plane x + 2y + 3z = 6 contains the points
A(6,0,0); B(0,3,0); and C(0,0,2).

The center of the circle circumscribing the points will be the intersection of the bisecting planes of the sides of the triangle with the plane of the triangle.

AB
vector AB = <-6, 3, 0> or <2, -1, 0>
midpoint M(3, 3/2, 0)
Bisecting plane
2(x - 3) - (y - 3/2) = 0
2x - 6 - y + 3/2 = 0
4x - 12 - 2y + 3 = 0
4x - 2y = 9

AC
vector AC = <-6, 0, 2> or <3, 0, -1>
midpoint M(3, 0, 1)
Bisecting plane
3(x - 3) - 1(z - 1) = 0
3x - 9 - z + 1 = 0
3x - z = 8

The center of the circle is the intersection of the three planes:

x + 2y + 3z = 6
4x - 2y = 9
3x - z = 8

Center (h, k, p) = (39/14, 15/14, 5/14)

r = radius
r² = (39/14 - 6)² + (15/14)² + (5/14)² = 2275/196
r = √(2275/196) = 5√91 / 14 ≈ 3.4069

The circumcircle of the points A, B, and C is the intersection of the plane

x + 2y + 3z = 6

with the sphere

(x - h)² + (y - k)² + (z - p)² = r²
(x - 39/14)² + (y - 15/14)² + (z - 5/14)² = 2275 / 196

Answer 2

x=6
y=3
z=2

gravity center is the center of the circle
(Hint: divide the sum by 3)

Circle equation(x-x1)^2+(y-y1)^2=r^2
satisy A,B,C points