Answer :
To determine the best definition of a conic section among the given options, let's analyze each one and see how well it aligns with the concept of conic sections:
A. A line that has a certain steepness and intersects the y-axis
This description is actually that of a linear equation or a straight line, which is not a conic section.
B. A curve resulting from the intersection of a right circular cone and a plane
This is the classical and most accurate definition of a conic section. When a plane intersects a right circular cone, depending on the angle of the intersection, several different types of curves can be produced: ellipses, parabolas, and hyperbolas.
C. A graph resulting from the intersection of a square-based pyramid and a plane
This description would suggest different geometric shapes that are not related to conic sections, which are specifically the result of the intersection with a right circular cone rather than a pyramid.
D. The side opposite a right angle in a right triangle
This defines the hypotenuse of a right triangle, which is unrelated to conic sections.
After carefully considering each option, the best and correct definition of a conic section is:
B. A curve resulting from the intersection of a right circular cone and a plane
A. A line that has a certain steepness and intersects the y-axis
This description is actually that of a linear equation or a straight line, which is not a conic section.
B. A curve resulting from the intersection of a right circular cone and a plane
This is the classical and most accurate definition of a conic section. When a plane intersects a right circular cone, depending on the angle of the intersection, several different types of curves can be produced: ellipses, parabolas, and hyperbolas.
C. A graph resulting from the intersection of a square-based pyramid and a plane
This description would suggest different geometric shapes that are not related to conic sections, which are specifically the result of the intersection with a right circular cone rather than a pyramid.
D. The side opposite a right angle in a right triangle
This defines the hypotenuse of a right triangle, which is unrelated to conic sections.
After carefully considering each option, the best and correct definition of a conic section is:
B. A curve resulting from the intersection of a right circular cone and a plane
