An ellipse is produced.
If I understand your description correctly, a line.
When a cone is sliced parallel to the base then the shape produced is a circle. If the cone is sliced at an angle so that the cut goes completely through the cone then an ellipse is produced. If the cut is made perpendicular to the cone's base then the shape produced is a parabola.
It would look like a straight vertical line, i.e. parallel to the y-axis, passing through the point on the x-axis where x=3.
Y = 2 The graph is a horizontal line passing through the point Y=2 on the Y=axis. The line is parallel to the X-axis, and exactly 2 units above it everywhere.
Conics, or conic sections, are the intersection of a plane with an infinite double cone. If that plane cuts both cones, it is a hyperbola. If it is parallel to the edge of the cone, you get a parabola. If neither is the case, it is an ellipse. The ellipse is also a circle if the plane is perpendicular to the altitude of the cone. Note that none of these are the case if the plane passes through the vertex of the cone.
A line is produced
An Ellipse
When a right circular cone is intersected by a plane that passes through one vertex (nape) of the cone and is not parallel to any edge, the resulting shape is a parabola. This occurs because the plane cuts through the cone in such a way that it creates a curved section, which is characteristic of a parabola. The specific orientation and angle of the plane will determine the exact dimensions and location of the parabola within the cone.
If I understand your description correctly, a line.
When a right circular cone is intersected by a plane that passes through its vertex and touches the edge of each nappe, the resulting shape is a triangle. This triangle is formed by the intersection line extending from the vertex to the edges of the cone's surfaces, effectively creating a triangular cross-section of the cone.
It will be a hyperbola.
hyperbola
hyperbola
If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
CIRCULAR
Providing that the lines are parallel that the transversal passes through then it will have two equal alternate angles that are on opposite sides of the transversal.
When it is produced it is processed through a tube, giving it a circular shape.