Sphere Tangent to a Plane and Passing Through a Point

Sphere Tangent to a Plane and Passing Through a Point

For centre $$C(a,b,c)$$ and radius $$r$$, the conditions are:

$$\frac{|Aa+Bb+Cc+D|}{\sqrt{A^2+B^2+C^2}}=r$$

and:

$$(x_1-a)^2+(y_1-b)^2+(z_1-c)^2=r^2$$

Usage

- Used to determine unknown sphere parameters subject to tangency and point conditions.