Mathematics

Problem

73. Graphing Lines Using Polar Equations (a) Explain why

r=a \sec \theta

is a polar form for the line

x=a

. (b) Explain why

r=b \csc \theta

is a polar form for the line

y=b

. (c) Let

y=m x+b

. Prove that

r=\frac{b}{\sin \theta-m \cos \theta}

is a polar form for the line. What is the domain of

r

? (d) Illustrate the result in part (c) by graphing the line

y=2 x+3

using the polar form from part (c).