Question

How do you convert x=3 into a polar equation?

Answer 1

`r=3 sec theta`.

Explanation:

`x=r cos theta`
So, x =3 becomes `r cos theta = 3 or r = 3 sec theta`

x = 3 is the straight line parallel to y-axis, in the first and fourth quadrants, at a distance 3 from the y-axis.

The polar forms of lines parallel to the axes are `r = a sec theta, theta in (-pi/2, pi/2) and r = a csc theta, theta in (pi, 0)`.
r ranges from `+oo` down to a and increase to `+oo`.

Unless necessitated (in problems relating to radial directions), polar forms are avoided for equations of straight lines . .