37-50 Finding the equation of a Hyperbola Find an equation for the hyperbola that satisfies the given conditions.
Vertices , hyperbola passes through
The equation for the hyperbola with vertices , and the it passes through .
The vertices are , and the hyperbola passes through .
The general equation of a hyperbola with -axis as the transverse axis is given by
The length of the transverse axis is
Here, is the transverse axis, is the conjugate axis, c is the focus, is the center of the hyperbola, and is the length of the transverse axis.
Since the vertices are .
Use the midpoint formula to find and .
From the equation , the length of the transverse axis is
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