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Chapter 9: Q. 12. (page 771)

The directrices of the hyperbola with equation y2B2-x2A2=1are the lines with equations x=卤Ae, where e is the eccentricity of the hyperbola. What are the equations for the directrices of the hyperbola with equation y2B2-x2A2=1

Short Answer

Expert verified

The required answer y=Be,y=-Bewhere eis the eccentricity of the hyperbola.

Step by step solution

01

Given information

The given hyperbola isy2B2-x2A2=1

02

The objective is to write the directrices of the hyperbola.

A hyperbola is a set of points in a plane whose distances to two fixed points in the plane have a constant difference. It is a curve with two distinct and similar branches.

Every hyperbola has two directrices.

The directrices of the hyperbola y2B2-x2A2=1are the horizontal lines.

They are y=Beand y=-Bewhere eis the eccentricity of the hyperbola.

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Most popular questions from this chapter

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

One petal of the polar roser=cos4胃

Explain why there are infinitely many different hyperbolas with the same foci.

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

x=0

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

directrixx=-1,focus(2,5)

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

y=x
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