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Given a set of 2 spheres, how can one find the plane tangental to the intersection point of the spheres?

Suppose I have the following input

Vector3 sphere1 = new Vector3(8, 6, 2);
float radius1 = 5f;

Vector3 sphere2 = new Vector3(5, 3, 8);
float radius2 = 8f;

How can I get the following outpout:

Vector3 planePosition;
Vector3 planeNormal;

Most solutions I found online use linear algebra jargon that I find hard to understand and put some code functions behind. I'd appreciate it if someone could try to help me out

Tea-F-Tea
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    I think, most general case, intersection of 2 spherical surfaces shapes a circle. What is the really wanted? Can you show with figure? – fana Nov 10 '22 at 01:52
  • I'd like to calculate the intersection point of 4 spheres, a proposed method I found online is to subtract the sphere equations from another, resulting in 3 different planes that could intersect at some point. I just dont know how to achieve that, I know that the normal is found by sqrt((dot(point 1 - point2)), but I dont know how to find the point of intersection – Tea-F-Tea Nov 10 '22 at 09:25

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