What line forms when a plane and a cylinder intersect?

The line that forms when a plane intersects with a cylinder can vary depending on the angle at which the plane cuts through the cylinder. There are typically three scenarios:

1. If the plane cuts perpendicular to the cylinder's axis, the intersection line will be a circle. This is because the plane is slicing through the circular cross-sectional area of the cylinder.

2. If the plane cuts parallel to the axis of the cylinder and the cut goes through the side of the cylinder (not along its length), the intersection line will be a rectangle. This is due to the plane slicing through the cylindrical surface parallel to its axis, creating a rectangular shape.

3. If the plane cuts at an oblique angle (not perpendicular or parallel) to the cylinder's axis, the intersection line will typically be an ellipse. An ellipse is a geometric shape that looks like a stretched or squished circle. This result occurs because the oblique angle of the cut skews the circular cross-section of the cylinder into an elliptical shape.