Solving For a Sphere's Equation Given a Point of Intersection, as well as the centre.

Hi everyone,

The question is, "Find the equation of the sphere that psses through the origin with centre at (1,-2, 5)."

The equation of a sphere is: (X-j)^2 + (Y-k)^2 + (Z-L)^2 = r^2, where the centre is (j,k,L).

Would the problem be solved by replacing the Xs, Ys, and Zs with 0, and replacing jkL with (1,-2,5), respectively, and solving for r?

Thanks in advance!

Yes. Visualise it, though, so you see why. See the sphere centred at (1, -2, 5), maybe with an uncertain or fluctuating radius at first, but then fixed so that it passes through the origin. How would you find r, then?

That is exactly the same as finding the distance between (1, -2, 5), the center, and (0, 0, 0), a point on the sphere- which is, after all, the definition of "radius" of a sphere.