conic sections. शंकु परिच्छेद

conic sections. शंकु परिच्छेद #conicsections #circle #parabola #hyperbola #ellipse #mathsproject


Introduction to Conic Sections
By definition, a conic section is a curve obtained by intersecting a cone with a plane. In Algebra II, we work with four main types of conic sections: circles, parabolas, ellipses and hyperbolas. Each of these conic sections has different characteristics and formulas that help us solve various types of problems.

How to generate a circle, ellipse, parabola, and hyperbola by intersecting a cone with a plane?
Name each of the 4 conics.
Demonstrate how the conics are formed by a plane and a cone.
The fixed line is called the axis of the cone.
The vertex is the point shared by both cones.
The lines that pass through the vertex and form the cones are the generators. The generators lie in the cone.
The cone consists of two parts called the nappes.
A conic section section is a curve generated by intersecting a right circular cone with a plane.
A circle is generated when the plane is perpendicular to the axis of the cone.
An ellipse is generated when the plane is tilted so it intersects each generator, but only intersects one nappe.
A parabola is generated when the plane is tilted so it is parallel to one generator and only intersects one nappe.
A hyperbola is generated when the plane intersect both nappes.