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
If I understand your description correctly, a line.
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
When it is produced it is processed through a tube, giving it a circular shape.
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.
If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe, the shape produced is a line. Not asked, but... If the angle of the plane is less than the angle of the cone, then the intersection is a point. If the angle of the plane is greater than the angle of the cone, then the intersection is two lines intersecting at the vertex. If the plane insersects at other than the vertex, then the intersection is a circle when the plane is perpendicular to the cone's axis, an ellipse when the plane's angle is less than the cone's angle, a parabola when the planes's angle equals the cone's angle, and two hyperbole's in the last case.
parabola