Find Standard Equation of Hyperbola Given Foci: (-8,0) and (8,0) and Vertices: (-6,0) and (6,0).

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.

[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

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Originally Posted by ebaines

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.

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:confused:

Find the equation for the hyperbola that satisfies the given conditions? For Vertices(0, + or - 7) asymptote y= +or - 1/4.