UNIT 8 - OBJECTIVE 4 - HYPERBOLA

		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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