A hyperbola is a conic section obtained on slicing a double napped cone by a plane parallel to the axis of the cone. The locus of a point from a fixed point is at a constant ratio and it is greater than one of its distance from a fixed line is called a Hyperbola.
Standard form of a hyperbola: x^2/a^2 – y^2/b^2 = 1
Hyperbola Properties Explained
Below are explained the properties of hyperbola:
The lines from the foci to any point on a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.
The hyperbola is symmetric about x-axis, y-axis and hence the hyperbola is symmetric about the origin.
The hyperbola does not pass through the origin.
The tangent from any point (x1, y1) to the hyperbola is xx1/a2 – yy1/b2 = 1
I have recently faced lot of problem while learning Geometry Math, But thank to online resources of math which helped me to learn myself easily on net.
Important Hyperbola definitions
Focus: The fixed point is called a focus F1 (ae, 0) of the hyperbola.
Directrix : The fixed line is called the directrix of the hyperbola and its equation is x = a/e .
Transverse axis: The line segment AA' joining the vertices is called the transverse axis and the length of the transverse axis is 2a. The equation of transverse axis is y = 0.
Conjugate axis: The line segment joining the points B(0, b) and B'(0, - b) is called the conjugate axis. The length of the conjugate axis is 2b. The equation of the conjugate axis is x = 0
Centre: The point of intersection of the transverse and conjugate axes of the hyperbola is called the centre of the hyperbola. Here C(0, 0) is called the centre of the hyperbola.
Vertices: The points of intersection of the hyperbola and its transverse axis are called its vertices. The vertices of the hyperbola are A(a, 0) and A'(- a, 0).
Standard form of a hyperbola: x^2/a^2 – y^2/b^2 = 1
Hyperbola Properties Explained
Below are explained the properties of hyperbola:
The lines from the foci to any point on a hyperbola make equal angles with the tangent at that point. Hence if the surface of a reflector is generated by revolving a hyperbola about its transverse axis, all rays of light converging on one focus are reflected to the other.
The hyperbola is symmetric about x-axis, y-axis and hence the hyperbola is symmetric about the origin.
The hyperbola does not pass through the origin.
The tangent from any point (x1, y1) to the hyperbola is xx1/a2 – yy1/b2 = 1
I have recently faced lot of problem while learning Geometry Math, But thank to online resources of math which helped me to learn myself easily on net.
Important Hyperbola definitions
Focus: The fixed point is called a focus F1 (ae, 0) of the hyperbola.
Directrix : The fixed line is called the directrix of the hyperbola and its equation is x = a/e .
Transverse axis: The line segment AA' joining the vertices is called the transverse axis and the length of the transverse axis is 2a. The equation of transverse axis is y = 0.
Conjugate axis: The line segment joining the points B(0, b) and B'(0, - b) is called the conjugate axis. The length of the conjugate axis is 2b. The equation of the conjugate axis is x = 0
Centre: The point of intersection of the transverse and conjugate axes of the hyperbola is called the centre of the hyperbola. Here C(0, 0) is called the centre of the hyperbola.
Vertices: The points of intersection of the hyperbola and its transverse axis are called its vertices. The vertices of the hyperbola are A(a, 0) and A'(- a, 0).
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