This is a free lesson from our course in Algebra II
This lesson covers important basics of a hyperbola like the
foci,
center,
asymptotes etc. Further you'll learn how to identify the
key elements and graph the hyperbola. Hyperbola is a
curve resulting from the
intersection of a plane with
cone such that the set of all points in the plane,
the difference of whose distances from two fixed points (the foci) remains constant.
The center of a hyperbola is the midpoint of the segment connecting the foci. An
asymptote of hyperbola is a line whose distance to the curve tends to zero. If a
hyperbola has x axis as a major axis and y as the minor axis,
then equation of the hyperbola in standard form is:
(x  h)^{2}/a^{2}
 (y  k)^{2}/b^{2} = 1,
where (h, k) is the center of hyperbola.
(More text below video...)
(Continued from above)The vertex is a point at which a hyperbola makes its sharpest
turns; coordinates of vertices are:
(a,
0).
Coordinates of foci are:
(c,
0),
where c is the distance from center to foci.
This all may appear to be bit difficult to understand but you'll find some examples
with solution, and the instructor explains all that with the help of audio, video
presentation and in own hand writing that makes it learn easy.
Take a look at the equation of hyperbola x^{2}/9 
y^{2}/16 = 1,
Vertices are: (3,
0)
Foci are: (5,
0)
Equation of asymptotes are y =
(4/3)x.
Another standard form of hyperbola, when the center is origin (0, 0), is
x^{2}/a^{2}
+ y^{2}/b^{2} = 1.
Coordinates of vertices are: (0,
b).
Foci are (0,
c).
Equation of the asymptotes are: y =
(b/a)x.
E.g. In equation of hyperbola x^{2}/6  y^{2}/3 =1, vertices are
(0,
3),
foci are (0,
5),
and equation of asymptotes are y=
(1/2)x.
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