Algebra II: Graphing the Equation of a Hyperbola
 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/a2 - (y - k)2/b2 = 1, where (h, k) is the center of hyperbola.  (More text below video...)
Other useful lessons:
 Completing the square Graphing the equation of a circle Graphing the equation of a parabola Calculating the asymptotes Conic sections and special points
(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
x2/9 - y2/16 = 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
-x2/a2 + y2/b2 = 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 x2/6 - y2/3 =-1, vertices are (0, 3), foci are (0, 5), and equation of asymptotes are y=  (1/2)x. Winpossible's online math courses and tutorials have gained rapidly popularity since their launch in 2008. Over 100,000 students have benefited from Winpossible's courses... these courses in conjunction with free unlimited homework help serve as a very effective math-tutor for our students.
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