Conics type and orientation refer to the shape and orientation of a conic section, which is a curve formed by the intersection of a cone with a plane. The type of conic depends on the angle at which the plane intersects the cone, and the orientation refers to the direction in which the curve opens.
The five types of conics are parabolas, circles, ellipses, hyperbolas, and degenerate conics. Parabolas have one focus and one directrix, circles have a constant distance from a center point, ellipses have two foci, hyperbolas have two branches that open in opposite directions, and degenerate conics are formed when the plane intersects the cone at a specific angle.
Conics can be classified as either vertical or horizontal orientation. A vertical conic has a major axis that is parallel to the y-axis, and a horizontal conic has a major axis that is parallel to the x-axis.
The eccentricity of a conic is a measure of how "squished" or elongated the curve is. It is calculated as the distance between the foci divided by the length of the major axis. A higher eccentricity indicates a more elongated shape, while a lower eccentricity indicates a more circular shape.
Conic sections have numerous real-life applications, such as in astronomy to describe the orbits of planets, in engineering to design parabolic reflectors for satellite dishes, in architecture to create dome structures, and in optics to model the shape of lenses. They are also used in sports, such as in the trajectory of a baseball or a golf ball.