Answer:
Step-by-step explanation:
Be the points Pa=(-1,-6,-8) ; Pb=(0,-4,-5) we have calculate the middle point or center
[tex]c=(\frac{x1+x2}{2}, \frac{y1+y2}{2}, \frac{z1+z2}{2})=(\frac{-1}{2}, -5,\frac{-13}{2})[/tex]
Now we must to find d=r (view graph)
[tex]r=\sqrt{(Cx-x2)^{2}+(Cy-y2)^{2}+(Cz-z2)^{2}}\\ r=\sqrt{(\frac{-1}{2} )^{2}+(-5+4)^{2}+(\frac{-13}{2}+5 )^{2}}\\r=\sqrt{\frac{1}{4} +1+\frac{9}{4}}=\sqrt{\frac{14}{4}}=r^{2}=\frac{14}{4}[/tex]
We find the canonical sphere equation
[tex](x-h)^{2}+(y-k)^{2}+(z-l)^{2}=r^{2}\\(x+\frac{1}{2})^{2}+(y+5)^{2}+(z+\frac{13}{2} )^{2}=\frac{14}{4}\\x^{2}+x+y^{2}+10y+z^{2}+13z+64=0[/tex]
Note: The Pa=(-1,-6,-8) can also be used in c
