Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).

Result

r =  3.94
x0 =  1.489
y0 =  1.191
z0 =  -2.234

Solution:

3x+2z=0 4x5y=0 r2=(x0)2+(y+2)2+(z+4)2 r2=(x2)2+(y+1)2+(z1)2  (xx0)2+(yy0)2+(zz0)2=r2  r>0  r=34289/473.9398=3.943x+2z=0 \ \\ 4x-5y=0 \ \\ r^2=(x-0)^2 + (y+2)^2 + (z+4)^2 \ \\ r^2=(x-2)^2 + (y+1)^2 + (z-1)^2 \ \\ \ \\ (x-x_{0})^2+(y-y_{0})^2+(z-z_{0})^2=r^2 \ \\ \ \\ r>0 \ \\ \ \\ r=\sqrt{ 34289 }/47 \doteq 3.9398=3.94
x0=70/47=70471.48941.489x_{0}=70/47=\dfrac{ 70 }{ 47 } \doteq 1.4894 \doteq 1.489
y0=56/47=56471.19151.191y_{0}=56/47=\dfrac{ 56 }{ 47 } \doteq 1.1915 \doteq 1.191
z0=105/47=105472.234z_{0}=-105/47=- \dfrac{ 105 }{ 47 } \doteq -2.234



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