A conic section is a curve formed when a plane cuts a cone in different ways. The shape created depends on the angle of the cut, producing curves such as a circle, ellipse, parabola, and hyperbola. These curves play an important role in geometry and many real-world applications.
Each type of conic section has unique properties and equations, making them essential for understanding orbital mechanics, designing optical systems, and solving quadratic equations
Foundations
Build a strong understanding of the basic concepts and properties that form the base of all conic sections.
- Introduction to Conic Sections
- Eccentricity
- Directrix
- Latus Rectum
- Focal Chord
- Identifying Conic Sections from their Equation
- Degenerate and Non-Degenerate Conics
- Real-Life Applications
Circle (e = 0)
A circle is the simplest conic section where every point on the curve is at an equal distance from a fixed center.
- Introduction to Circles
- Parts of a Circle
- Equation of a Circle (Standard & General Form)
- Formulas
- Chord of a Circle
- Arc
- Sector of a Circle
- Tangent to a Circle
- Secant of a Circle
- Concentric Circles
- Quiz
Parabola (e = 1)
A parabola is a smooth, open curve formed when a point moves equally distant from a fixed point and a fixed line.
- Introduction to Parabola
- Standard Equation
- Focus and Directrix of a Parabola
- Vertex
- Tangents and Normals to a Curve
- Axis of Symmetry
- Quiz
- Applications of Parabola
Ellipse (0 < e < 1)
An ellipse is a closed curved shape formed when the sum of distances from two fixed points remains constant.
- Introduction to Ellipse
- Ellipse Formula
- Eccentricity
- How to Find the Equation of an Ellipse
- Application of Ellipse
Hyperbola (e > 1)
A hyperbola is an open curve with two branches formed when the difference of distances from two fixed points remains constant.