Odd One Out: Circle

Explanation:
When we compare the given options, we can see that all the options except the circle are different types of conic sections.

Definition of Conic Sections:
A conic section is a curve that can be formed by intersecting a cone with a plane. There are four types of conic sections:
1. Pair of lines
2. Hyperbola
3. Parabola
4. Circle

Explanation of the Options:
a) Pair of lines:
A pair of lines is formed when a plane intersects a cone in such a way that it intersects both halves of the cone. The intersection results in two distinct lines.

b) Hyperbola:
A hyperbola is formed when a plane intersects a cone in such a way that it intersects both halves of the cone but does not pass through the apex. The intersection results in a curve with two separate branches.

c) Parabola:
A parabola is formed when a plane intersects a cone in such a way that it intersects one half of the cone and is parallel to the other half. The intersection results in a curve with a single branch.

d) Circle:
A circle is formed when a plane intersects a cone in such a way that it intersects both halves of the cone and is equidistant from the apex. The intersection results in a closed curve with all points on the curve at the same distance from the center.

Difference of Circle:
The main difference between a circle and the other conic sections is that a circle is a closed curve, while the other conic sections are open curves. A circle is also the only conic section that has all points on the curve at the same distance from the center.

Therefore, the odd one out among the given options is the circle because it is the only conic section that is a closed curve and has all points at the same distance from the center.