Understanding Conic Sections
Conic sections are curves obtained by intersecting a cone with a plane. The type of curve formed depends on the angle of the intersecting plane. The primary conic sections include circles, ellipses, parabolas, and hyperbolas.
Why Circle is a Conic Section
- A circle is formed when the intersecting plane is perpendicular to the axis of the cone.
- It is defined as the set of all points in a plane that are equidistant from a fixed point (the center).
- The general equation of a circle in a Cartesian plane is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Characteristics of Other Options
- Rectangle: A rectangle is a quadrilateral with opposite sides equal and does not fit the definition of a conic section.
- Triangle: A triangle is a three-sided polygon and is not derived from the intersection of a cone.
- Square: A square is a specific type of rectangle with equal sides and right angles, but it too is not a conic section.
Conclusion
In summary, among the given options, only a circle qualifies as a conic section due to its geometric properties derived from the intersection of a cone with a plane. The other shapes listed—rectangle, triangle, and square—are simple polygons and do not have the characteristics that define conic sections.