   Chapter 10.1, Problem 48E

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. Focus : ( 20 , 0 ) Asymptotes   : y = ± 3 4 x

To determine

To calculate: The standard equation of hyperbola with the help of provided characteristics.

Explanation

Given:

The characteristics of the hyperbola are: Focus (20,0) and Asymptotes: y=±34x.

Formula used:

The equation of the asymptotes of the hyperbola of first kind is, y=k±ba(xh) and the Eccentricity is given by, e=1+(ba)2

Calculation:

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 (xh)2a2(yk)2b2=1.

The provided equation of asymptotes is y=±34x

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