The sphere centered at the point O (0; 1; -2) passes through the point A (-3; 1; 2) a) Make the equation of the sphere

The sphere centered at the point O (0; 1; -2) passes through the point A (-3; 1; 2) a) Make the equation of the sphere b) Find the coordinates of the points of the abscissa axis belonging to the given sphere.

Distance from the center of the sphere O to point A:

((-3 – 0) ^ 2 + (1 -1) ^ 2 + (2 – (-2)) ^ 0.5 = (9 + 0 + 16) ^ 0.5 = 5.

5 – radius of the sphere and its equation:

(x – 0) ^ 2 + (y – 1) ^ 2 + (z – (-2)) ^ 2 = 5 ^ 2 or

x ^ 2 + (y -1) ^ 2 + (z + 4) ^ 2 = 25 or

x ^ 2 + y ^ 2 + z ^ 2 – 2y + 8z = 8.

On the abscissa axis y = 0 and z = 0. Substituting these values into the equation of the sphere, we obtain

x ^ 2 + 0 ^ 2 + 0 ^ 2 – 2 * 0 + 8 * 0 = 8,

x ^ 2 = 8,

x = 2 * 2 ^ 0.5 or x = -2 * 2 ^ 0.5.

The coordinates of the points of intersection of the sphere with the abscissa axis:

(2 * 2 ^ 0.5; 0; 0) and (-2 * 2 ^ 0.5; 0; 0).