6. Conic Sections
Conic sections are curves resulting from the intersection of a plane with a double-napped cone, encompassing circles, parabolas, ellipses, and hyperbolas. This chapter details their definitions, standard equations, properties, and significance in coordinate geometry.
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What we have learnt
- Conic sections are defined based on their geometric properties and interrelations with a cone.
- Each type of conic section has a unique standard equation and distinctive geometric features.
- Understanding conic sections is essential for applications in engineering, physics, and mathematics.
Key Concepts
- -- Conic Sections
- Curves derived from slicing a cone with a plane, resulting in circles, parabolas, ellipses, and hyperbolas.
- -- Circle
- A set of points equidistant from a central point, characterized by its radius.
- -- Parabola
- A curve representing all points equidistant from a fixed point (focus) and a fixed line (directrix).
- -- Ellipse
- A shape formed by points where the sum of distances from two foci is constant.
- -- Hyperbola
- A curve where the difference in distances to two foci is constant.
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