   Chapter 10, Problem 122RE

Chapter
Section
Textbook Problem

# Finding a Polar Equation In Exercises 119-122, find a polar equation Tor the conic with its focus at the pole and the Risen eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.) Conic Eccentricity Directrix Hyperbola e   = 5 2 r   =   − 1

To determine

To calculate: A polar equation of the hyperbola whose focus is at the pole, eccentricity is e=52 and directrix is x=1.

Explanation

Given:

The hyperbola has eccentricity e=52 and directrix x=1 and focus is at the pole.

Formula used:

Equation of a hyperbola in the polar form is r=ed1ecosθ; where d is the focus and e is eccentricity.

Calculation:

Consider a hyperbola with eccentricity e=52 and directrix x=1. Also, the focus is at the pole, d=|1| or d=1. Here, the directrix is a line parallel to the y-axis. Therefore, the standard equation of the conic is:

r=ed1ecosθ

Substitute the values of e and d

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