19/07/2025
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CONIC SECTIONS:
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.
History:
Conic Sections ( Circle, Ellipse, Parabola and Hyperbolas) were first studied by ancient Greek mathematicians, with Menaechmus credited as the earliest discoverer around 350 BCE while working on the problem of doubling the cube. These curves were further investigated by Euclid, Archimedes, and later by Apollonius of Perga, who is known for his comprehensive work on conics in his eight-book series. Later, mathematicians like Pappus, Omar Khayyam, and even Descartes contributed to the understanding and application of conic sections.
Basic Definition:
CONIC SECTIONS
•A conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane; the three types are parabolas, ellipses, and hyperbolas. A conic section can be graphed on a coordinate plane. Every conic section has certain features, including at least one focus and directrix. Parabolas have one focus and directrix, while ellipses and hyperbolas have two of each.
- Circle
•A circle is the set of all points in a plane that are equidistant from a fixed point called the center.
- Parabola
•A parabola is the set of all points in a plane that are equidistant from a fixed point (focus) and a fixed line (directrix).
- Ellipse
•An ellipse is the set of all points in a plane where the sum of the distances from two fixed points (foci) is constant.
- Hyperbola
•A hyperbola is the set of all points in a plane where the absolute difference of the distances from two fixed points (foci) is constant.
Properties and formula:
📐 C