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!

Re: Solving For a Sphere's Equation Given a Point of Intersection, as well as the cen

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?

Re: Solving For a Sphere's Equation Given a Point of Intersection, as well as the cen

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.