(a) Show that if a varies, then the polar equationr = a sec (/2 <</2)describes a family

Chapter 10, Problem 59

(choose chapter or problem)

(a) Show that if $a$ varies, then the polar equation

$r=a \sec \theta \quad(-\pi / 2<\theta<\pi / 2$

describes a family of lines perpendicular to the polar axis.

(b) Show that if $b$ varies, then the polar equation

$r=b \csc \theta \quad(0<\theta<\pi)$

describes a family of lines parallel to the polar axis.

Equation Transcription:

$a$

$r=a\ sec\ \theta{}\ \ \ \ \ \ \ \ \ (-\pi{}/2<\theta{}<\pi{}/2$

$b$

$r=b\ csc\ \theta{}\ \ \ \ \ (0<\theta{}<\pi{})$

Text Transcription:

r=a sec theta(-pi/2<theta<pi/2

r=b csc theta (0<theta<pi)

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