Final answer:
When a plane that bisects the axis of a right circular cone and is inclined to the HP cuts the cone, the section obtained is an ellipse, due to the constant sum of distances to two fixed points (foci) that define an ellipse.
Step-by-step explanation:
The student's question relates to determining the true shape of a section obtained by cutting a right circular cone with a plane that bisects its axis and is inclined to the horizontal plane (HP). In the context of conic sections, the intersection of a plane with a cone can result in different shapes such as a circle, ellipse, parabola, or hyperbola.
However, when the cutting plane bisects the axis of a right circular cone and is inclined to the HP, the resulting figure is an ellipse. This is because an ellipse is defined as the set of all points for which the sum of distances to two fixed points (foci) is constant.
Since the section plane bisects the cone's axis symmetrically, the distances to the foci are equal at all points of the cross-section, making it an ellipse, not a perfect circle with a single central focus, nor a parabola or hyperbola which require different conditions for their formation.