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:


\frac { (x-x_0)^2 } {a^2} - \frac { (y-y_0)^2 } {b^2} = 1


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 x_0 and y_0 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:


e = sqrt {1 + \frac {b^2} {a^2}}


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

A standard form of the equation for a hyperbola is:


\frac { (x-x_0)^2 } {a^2} - \frac { (y-y_0)^2 } {b^2} = 1


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 x_0 and y_0 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:


e = sqrt {1 + \frac {b^2} {a^2}}


So from this you should be able to determine b.

:confused:

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