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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