   Chapter 10.6, Problem 33E

Chapter
Section
Textbook Problem

Finding a Polar Equation In Exercises 33-38, Find a polar equation for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form)Conic Eccentricity DirectrixParabola e = 1 x = − 3

To determine

To calculate: The polar equation for the parabola having its focus at the pole and the eccentricity e=1 and the equation of directrix is x=3.

Explanation

Given:

The conic is parabola having:

The eccentricity: e=1

And the equation of directrix is: x=3

Formula used:

The polar form of the equation for the parabola having its focus at the pole is:

r=ed1ecosθ

Here, e is the eccentricity of the parabola and d is the distance from the focus and its directrix.

The standard equation of directrix is: x=d

Calculation:

The equation for directrix is: x=3

So,

x=d

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