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Tangent planes parallel to a given plane

Find the tangent planes to the surface (cylinder) parallel to the plane with normal (1, 2, 3).

Step-by-step solution

1. Parallel tangent planes have the same normal.
2. Move the plane until it touches the surface: there are two, one on each side.
3. On the sphere, the distance to the centre is the radius.
4. Check the points of tangency and that the plane does not cut the surface.

Result: 2 tangent plane(s). Cada plano toca al cilindro en un punto del borde de una base.

On the sphere there are always two; on the cone and cylinder, sometimes only one or none.

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