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The question asks for the definition of a circle as a conic section. Here are the answer choices given:

a. A set of all points in a plane that are equidistant to a fixed point and a fixed line.
  
b. It is formed when the plane and the side of the cone is PARALLEL to each other.

c. A set of all points in a plane that are equidistant from a fixed center point.

d. It is formed when the plane and the base of the cone is PARALLEL to each other.

### Correct Answer:
The correct answer is **c. A set of all points in a plane that are equidistant from a fixed center point**.

This is the standard definition of a circle. A circle is defined as the set of all points in a plane that are at a fixed distance (radius) from a fixed point (center). This definition aligns with the properties of a circle in both Euclidean geometry and in the context of conic sections.

### Follow-up Questions:
1. How does the definition of a circle change when considering it as a conic section?
2. Can you define other conic sections like ellipse, parabola, and hyperbola in a similar way?
3. Why is option a incorrect in the context of a circle?
4. What happens to the shape of a circle when the distance from the center point to any point on the circle is varied?
5. How is the equation of a circle derived from its definition?

### Tip:
When studying conic sections, it's useful to remember that they are all curves obtained by intersecting a plane with a cone. The angle at which the plane intersects the cone determines the type of conic section.

Definition of Circle as a conic section. Select one:

a. A set of all points in a plane that are equidistant to a fixed point and a fixed line.

b. It is formed when the plane and the side of the cone is PARALLEL to each other.

c. A set of all points in a plane that are equidistant from a fixed center point.

d. It is formed when the plane and the base of the cone is PARALLEL to each other.

Explore the definition of a circle as a conic section with detailed explanations of core concepts in geometry. Learn about the key mathematical principles involved, suitable for students in Grades 9-12.

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