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.
Center: (0, 0)
Vertex: (6, 0)
Focus: (10, 0)
To calculate: The standard equation of hyperbola with the help of provided characteristics.
Given: The characteristics of the hyperbola are: Centre (0, 0), vertex(6, 0), Focus(10, 0).
Calculation: Since the provided vertex has only x-coordinate, so the vertex must be lies on x-axis.
Hence, the required hyperbola is of the first type where the transverse axis is the x axis.
Now the centre of the hyperbola is (0, 0) and the distance from the centre to the vertex is 6. Thus, the value of .
Also, the focus is , so
Now, the value of c is
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