UNIT 8 - OBJECTIVE 4 - HYPERBOLA
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A hyperbola is the set of points in a plane for which the difference of
the distance of the points from two fixed points is a constant. The
standard equation with the center at (0,0) and the major axis on the
X-axis is-

The vertices are (-a,0) and (a,0).
The foci are (-c,0) and (c,0) where

The lines  are asymptote.

The standard equation with the center at (a,0) and major axis on the Y-axis is:

The vertices are (0,-a) and (0,a). The foci are (0,c) and (0,-c) where

The lines  are asymptotes.

Example 1
Sketch the hyperbola:

Divide by 9 to get 1 on the right

The vertices are  or (1.7,0) and (-1.7,0).

To find the foci use

So the foci are  or (3.46,0) and (-3.46,0).
The asymptotes are

Example 2
Write the equation of the hyperbola, center at the origin which passes
through the point  and has vectors (4,0).
Sketch given equation first

So a=4,

Now we have to find   so plug in the point

Example 3
Sketch the hyperbola

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