Mathematics

The key is recognizing that a sphere's center must satisfy two constraints: it lies somewhere on the positive $y$-axis (so the center is at $(0, b, 0)$ where $b > 0$), and the distance from that center to the given point must equal the radius. Use the distance formula to set up an equation and solve for $b$, then write the sphere's equation in standard form.

The key is recognizing that a sphere's center must satisfy two constraints: it lies somewhere on the positive $y$-axis (so the center is at $(0, b, 0)$ where $b > 0$), and the distance from that center to the given point must equal the radius. Use the distance formula to set up an equation and solve for $b$, then write the sphere's equation in standard form.