   Chapter 10.1, Problem 47E

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 ,   2 ) ,   ( 6 , 2 ) Asymptotes: y = 2 3 x y = 4 − 2 3 x

To determine

To calculate: The equation of hyperbola with the vertices (0,2),(6,2) and

asymptotes y=423x,y=23x.

Explanation

Given:

The characteristics of hyperbola: vertices are (0,2),(6,2) and asymptotes are

y=423x,y=23x.

Formula used:

The standard equation of hyperbola is, (xh)2a2(yk)2b2=1

Calculation:

Since the provided equation has x changing vertex in it.

Therefore, it is a hyperbola of the first type where the transverse axis is the xaxis.

Thus, the standard equation of hyperbola is given by (xh)2a2(yk)2b2=1.

Where a is the transverse axis and b is the conjugate axis and (h,k) is the centre of the hyperbola

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