Find the polar equation for the curve described by the following Cartesian equations.
a. y = 45
b. x2 + y2 = 36
c. x2 - y2 = 1
d. 4xy = 1
e. y = 3x + 2
f. 3x2 + 4y = 2
g. x2 + 2x + y2 - 4y - 25 = 0
Computers and graphing calculators offer a wonderful opportunity to experiment with the graphing of polar equations of the form r = 1(0). In some cases these aids require that the equations be recast in a parametric form. Since x = r cos θ = f (θ) cos θ and y = r sin θ = f (θ) sin θ, you can use the parametric graphing capabilities to graph x = f(t) cos t and y = f (t) sin t as a set of parametric equations