Can someone guide me for finding the equation of a sphere that passes through $M=(-1,2,4)$ and intersects the $OXY$ axis on the circle $(x-1)^2+(y-2)^2=4$
Sorry for the bad terms in English .
2026-03-30 08:58:29.1774861109
Finding the equation of a shpere with given intersections on the XY axes
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Hint:
You have find that the center of the sphere has coordinates $C=(1,2, z_C)$.
With a bit more effort you can find that the radius of the sfere is $R^2=4+z_C^2$.
Now use the given point in the equation $(x-x_C)^2+(y-y_C)^2+(z-z_C)^2=R^2$.