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    NinjaDoode's Avatar
    NinjaDoode Posts: 3, Reputation: 1
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    #1

    Nov 28, 2008, 10:25 AM
    Finding Standard Equation Of Hyperbola, Given Foci and Vertices.
    Find Standard Equation of Hyperbola Given Foci: (-8,0) and (8,0) and Vertices: (-6,0) and (6,0).
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Dec 1, 2008, 11:36 AM

    A standard form of the equation for a hyperbola is:



    First thing to note is the that the vertices in this problem are on the x axis, and equi-distant from the origin, so that tells you that the hyperbola is centered on (0,0), and hence the values of and are both 0.

    The value for a is the distance form the center to the vertices, so in this case a = 6. The focii are both at distance ae from the center, where e is defined as the eccentricity of the hyperbola, so now you can determine the value for e. But e is also defined in terms of the values for a and b:



    So from this you should be able to determine b.
    harpreet2616's Avatar
    harpreet2616 Posts: 2, Reputation: 1
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    #3

    Oct 3, 2010, 07:57 AM
    [QUOTE=NinjaDoode;1397796]Find Standard Equation of Hyperbola Given Foci: (-8,0) and (8,0) and Vertices: (-6,0) and (6,0).:confused:

    HOW I WILL TAKE THE VALUES OF VERTICES & FOCI IN TERMS OF 'a' & 'b' for hyperbola formulae
    harpreet2616's Avatar
    harpreet2616 Posts: 2, Reputation: 1
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    #4

    Oct 3, 2010, 08:02 AM
    Quote Originally Posted by ebaines View Post
    A standard form of the equation for a hyperbola is:



    First thing to note is the that the vertices in this problem are on the x axis, and equi-distant from the origin, so that tells you that the hyperbola is centered on (0,0), and hence the values of and are both 0.

    The value for a is the distance form the center to the vertices, so in this case a = 6. The focii are both at distance ae from the center, where e is defined as the eccentricity of the hyperbola, so now you can determine the value for e. But e is also defined in terms of the values for a and b:



    So from this you should be able to determine b.
    :confused:
    eulalio's Avatar
    eulalio Posts: 4, Reputation: 1
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    #5

    Nov 21, 2012, 04:33 PM
    Find the equation for the hyperbola that satisfies the given conditions? For Vertices(0, + or - 7) asymptote y= +or - 1/4.

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