A hyperbola is a type of conic section, which is a geometric shape formed by the intersection of a plane and a cone. It is defined as the set of all points in a plane, such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
The general equation of a hyperbola is given
by:
(x - h)² / a² - (y - k)² / b² = 1
Where (h, k) represents the center of the hyperbola, 'a' is the distance from the center to a vertex, 'b' is the distance from the center to the co-vertex, and the foci are located 'c' units away from the center, where c is related to 'a' and 'b' through the equation c² = a² + b².
A hyperbola has two branches, which are symmetric with respect to both the x-axis and y-axis. The transverse axis is the line passing through the center and the two vertices, while the conjugate axis is perpendicular to the transverse axis and passes through the center.
Hyperbolas have several important properties. The distance between the two foci is constant for any point on the hyperbola. The asymptotes of a hyperbola are the lines that the branches approach as they extend infinitely. The eccentricity of a hyperbola is a measure of how "flattened" or elongated it is and is given by the ratio c / a. The eccentricity of a hyperbola is always greater than 1.
Hyperbolas have applications in various fields, including physics, engineering, and astronomy. They are used to describe the orbits of planets and satellites, electromagnetic radiation patterns, and the behavior of electric fields in certain systems.
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HYPERBOLA
A hyperbola is a type of conic section, which is a geometric shape formed by the intersection of a plane and a cone. It is defined as the set of all points in a plane, such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
The general equation of a hyperbola is given
by:
(x - h)² / a² - (y - k)² / b² = 1
Where (h, k) represents the center of the hyperbola, 'a' is the distance from the center to a vertex, 'b' is the distance from the center to the co-vertex, and the foci are located 'c' units away from the center, where c is related to 'a' and 'b' through the equation c² = a² + b².
A hyperbola has two branches, which are symmetric with respect to both the x-axis and y-axis. The transverse axis is the line passing through the center and the two vertices, while the conjugate axis is perpendicular to the transverse axis and passes through the center.
Hyperbolas have several important properties. The distance between the two foci is constant for any point on the hyperbola. The asymptotes of a hyperbola are the lines that the branches approach as they extend infinitely. The eccentricity of a hyperbola is a measure of how "flattened" or elongated it is and is given by the ratio c / a. The eccentricity of a hyperbola is always greater than 1.
Hyperbolas have applications in various fields, including physics, engineering, and astronomy. They are used to describe the orbits of planets and satellites, electromagnetic radiation patterns, and the behavior of electric fields in certain systems.
a symentrical open curved form by intersection of a circular cone with a plane at a smaller angle with its axis than the side of cone. pls mark me as brainliest