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 standard equation of hyperbola with the help of provided characteristics.
The characteristics of the hyperbola are: Focus and Asymptotes: .
The equation of the asymptotes of the hyperbola of first kind is, and the Eccentricity is given by,
Since the provided focus has only x-coordinate, so the focus must be lies on x-axis. Hence, the required hyperbola is of the first type where the transverse axis is the x axis.
Thus, th standard equation of hyperbola is given by .
The provided equation of asymptotes is
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