Conic section is a curve obtained by the intersection of the surface of a cone with a plane.
In Analytical Geometry, a conic is defined as a plane algebraic curve of degree 2. That is, it consists of a set of points which satisfy a quadratic equation in two variables. This quadratic equation may be written in matrix form. By this, some geometric properties can be studied as algebraic conditions.
Thus, by cutting and taking different slices(planes) at different angles to the edge of a cone, we can create a circle, an ellipse, a parabola, or a hyperbola, as given below
Property of Ellipse to reflect sound and light is used in pulverizing kidney stones. The patient is laid in an elliptical tank of water. Kidney stones being at the other focus are concentrated and pulverized.
Whispering galleries at US Statutory capital and St. Paul’s Cathedral, London demonstrates the property of the ellipse that one’s whisper from one focus can be heard at the other focus by only a person to whom it is sent
Lens, monitors, and optical glasses are of hyperbola shape.
Conic or conical shapes are planes cut through a cone. Based on the angle of intersection, different conics are obtained. Parabola, Ellipse, and Hyperbola are conics. Circle is a special conic. Conical shapes are two dimensional, shown on the x, y axis. Conic shapes are widely seen in nature and in man-made works and structures. They are beneficially used in electronics, architecture, food and bakery and automobile and medical fields.
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Frequently Asked Questions (FAQs)
What are the 4 types of conic sections?
According to the angle of intersection between a plane and a cone, four different conic sections are obtained. They are Parabola, Ellipse, Hyperbola, and Circle. They are two dimensional on the x-y axis.
Conic section involves a cutting plane, surface of a double cone in hourglass form and the intersection of the cone by the plane. According to the angle of cutting, that is, light angle, parallel to the edge and deep angle, ellipse, parabola and hyperbola respectively are obtained. Circle is also conic, and it is cut parallel to the circular bottom face of the cone.