   Chapter 10.1, Problem 42E

Chapter
Section
Textbook Problem

# 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. Vertices : ( 0 , ± 4 ) Asymptotes   : y = ± 2 x

To determine

To calculate: The standard equation of hyperbola with the Vertices (0,±4) and asymptotes y = ±2x

Explanation

Given: The characteristics of the hyperbola are: Vertices (0,±4) and asymptotes y = ±2x

Calculation:

Since in the provided vertices only the value of y coordinate change. Thus, the provided hyperbola is of the second type where the transverse axis is the y axis.

So,

a=4or,a2=16

Now, the equation of asymptotes is given by the formula,

y=k±ab(xh)

from the provided equation of asymptote, it is clear that the hyperbola must be centred at origin, that means the centre of the required hyperbola will be 0, 0)

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