Finding the Standard Equation of a Hyperbola In Exercises 41-48, find the standard form of the equation of the hyperbola with the given characteristics.
To calculate: The equation of hyperbola with the vertices is and foci is .
The characteristics of a hyperbola are: vertices is and foci is .
The standard equation of parabola is, .
Since the given equation has y changing vertices in it.
Therefore, it’s a hyperbola of the second type (where the transverse axis is the ).
Now, the mid-point of both the vertices gives us the centre of the hyperbola is and the distance from centre to the vertex is 3.
Now the standard equation of hyperbola with as centre a and b as conjugate and
transverse axis is given by;
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