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No. A hyperbola is formed when a plane slices a cone perpendicular to the bases.
A parabola is the figure formed by the intersection of a circular cone and a plane that lies parallel to the edge of the cone. (the cone does not have to be a right [90°] circular cone).
It is a section formed by a plane at right angles to the axis of the cone.
The weight of the atmosphere presses down on the groundwater in the well
That can be an ellipse, circle, parabola, or hyperbola. It depends on the angle between the plane and the axis or surface of the cone.