Question 749831
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All hyperbolas that have equation

{{{x^2/a^2}}}{{{""-""}}}{{{y^2/b^2}}}{{{""=""}}}{{{1}}}

look like this:

{{{drawing(560,350,-14+20,14+20,-10+20,10+20,graph(560,350,-14+20,14+20,-10+20,10+20,sqrt(7(x-20)^2-252)/3+20),graph(560,350,-14+20,14+20,-10+20,10+20,-sqrt(7(x-20)^2-252)/3+20),

locate(19.6,21.1,O),
circle(8+20,0+20,.2),circle(-8+20,0+20,.2),circle(6+20,0+20,.2),circle(-6+20,0+20,.2),circle(6+20,0+20,.2),
green(line(6+20,sqrt(28)+20,6+20,-sqrt(28)+20),line(6+20,-sqrt(28)+20,-6+20,-sqrt(28)+20),line(-6+20,-sqrt(28)+20,-6+20,sqrt(28)+20),line(-6+20,sqrt(28)+20,6+20,sqrt(28)+20)),line(21+20,18.52+20,-22+20,-19.4+20),
line(21+20,-18.52+20,-22+20,19.4+20), triangle(-100,20,100,20,0,20),
locate(25.4,20.9,V), locate(27.4,20.9,F),locate(25.4-12.4,20.9,"V'"), locate(27.4-16.1,20.9,"F'"),triangle(20,-100,20,100,20,0),locate(0+20.2,6.2+20,P),locate(0+20.2,-5.2+20,Q)
)}}}

You won't have any trouble with hyperbolas if you learn all the parts
and what lengths "a", "b", and "c" stand for:

The RED CURVE with two non-connecting parts is the HYPERBOLA
The two slanted lines are the ASYMPTOTES
The green RECTANGLE is the DEFINING RECTANGLE
The VERTICES are the points V and V'
The FOCI (FOCAL POINTS) are F and F'
The CENTER is the point O. In your case the center is the origin (0,0)
but later you'll have some that have other centers.
The COVERTICES are P and Q
The TRANSVERSE AXIS is the line segment VV'. It's length is 2a
The CONJUGATE AXIS is the line segment PQ.  Its length is 2b
The SEMI-TRANSVERSE AXIS is either of the lines OV or OV'. It's length is a
The SEMI-CONJUGATE AXIS is either of the lines OA or OB. It's length is b

The FOCI (FOCAL POINTS) is "c" units from the center, that is,
the line segment OF is c units long.  

a, b, and c follow the Pythagorean theorem equation c² = a²+b²

Go here for some hyperbola questions. Be sure to click the related questions:
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http://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Quadratic-relations-and-conic-sections.faq.question.80329.html
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Edwin</pre>