hyperbola c
A hyperbola is a type of conic section, which is a curve formed by the intersection of a cone with a plane
A hyperbola is a type of conic section, which is a curve formed by the intersection of a cone with a plane. A hyperbola consists of two disconnected curves, also known as branches, that are symmetrical about the transverse axis.
The general equation of a hyperbola centered at the origin (0,0) is:
(x^2 / a^2) – (y^2 / b^2) = 1
where “a” represents the distance from the center to each vertex along the x-axis, and “b” represents the distance from the center to each vertex along the y-axis.
The center of the hyperbola is always at the origin (0,0), and the transverse axis is the line segment that passes through both vertices. It is parallel to the x-axis and has a length equal to 2a. The conjugate axis is the line segment perpendicular to the transverse axis, which also passes through the center of the hyperbola. It is parallel to the y-axis and has a length equal to 2b.
The distance between the center and each focus of the hyperbola is given by:
c = sqrt(a^2 + b^2)
The distance from the center to each directrix is also given by the value of “c”. The directrices are lines around the hyperbola that define its shape.
In summary, a hyperbola is a curve with two symmetrical branches, where the distance from the center to each vertex determines the shape and size. It has a transverse axis parallel to the x-axis, a conjugate axis parallel to the y-axis, and foci and directrices that play an important role in its properties and equations.
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