The hyperbola equation is .

hyperbola equation	\ \	\ \
Direction of transverse axis	horizontal	vertical
Equations of asymptotes		\ \

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•  Where, "a " is the number in the denominator of the positive term, If the x - term is positive, then the hyperbola is horizontal
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• a = semi - transverse axis , b = semi - conjugate axis
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• Center: (0, 0 )
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• Vertices: (a, 0 ) and ( a, 0 )
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• Foci: (c, 0 ) and (c, 0 )
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The hyperbola equation is .

Rewrite the equation as : .

Compare the above equation with .

a = semi - transverse axis = 3,

b = semi - conjugate axis = 5,

Center : (h, k ) = (0, 0), Vertices : (a, 0 ) and ( a, 0 ) = (3, 0) and ( 3, 0)

         (Substitute : a = 3 and b = 5)

Foci : (c, 0 ) and ( c, 0 ) =

Asymptotes of hyperbola are :  .

       (Substitute : h = 0, k =0 , a = 3, and b = 5)

Graph of hyperbola:

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• Draw the coordinate plane.
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• Plot the center of hyperbola (0, 0).
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• To graph the hyperbola go 5 units up and down from center point and 3 units left and right from center point.
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• Use these points to draw a rectangle .
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• Draw diagonal lines through the center and the corner of the rectangle. These are asymptotes.
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• The graph approaches the asymptotes but never actually touches them.
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• Draw the curves, beginning at each vertex separately, that hug the asymptotes the farther away from the vertices the curve gets.
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• Plot the vertices and foci of hyperbola.
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The center of the hyperbola is (0, 0), vertices are , foci are ,

asymptotes of the hyperbola are , and the graph is shown below :