Final answer:
The equation of an ellipsoid passing through two points can be found by substituting the coordinates of the points into the general equation of an ellipsoid and solving for the unknowns.
Step-by-step explanation:
The equation of an ellipsoid can be found using the equation:
(x-h)²/a²+ (y-k)²/b² + (z-l)²/c² = 1
where (h, k, l) represents the center of the ellipsoid and a, b, and c represent the semi major axes.
To find the equation of an ellipsoid passing through two given points, we need to substitute the coordinates of the points into the equation and solve for the unknowns h, k, l, a, b, and c.
For example, if the two points are (x1, y1, z1) and (x2, y2, z2), we substitute these points into the equation and solve the resulting system of equations.
Once we find the values for h, k, l, a, b, and c, we can write the equation of the ellipsoid in the form (x-h)²/a² + (y-k)²/b² + (z-l)²/c² = 1.