Question

How do you convert the rectangular equation $x = 4$ into polar form?

Answer 1

The equation $x = 4$ represents the line parallel to the $x$-axis whose $y$ values are $0$ in the rectangular coordinate.
The polar coordinate system is given by $(r,\theta )$ .
To convert a rectangular equation in polar form, the conversion equations of $x = r\cos \theta \;$ and $y = r\sin \theta \;$ are used.
Substitute $x = 4$ into the equation $x = r\cos \theta \;$ to get the required equation.

Complete step-by-step answer:
Convert the rectangular equation $x = 4$ into polar form. To convert a rectangular equation in polar form, the conversion equations of $x = r\cos \theta \;$ and $y = r\sin \theta \;$ are used.
Substitute $x = 4$into the equation $x = r\cos \theta \;$.
$4 = r\cos \theta \;$
$\Rightarrow r = \dfrac{4}{{\cos \theta }}$

Final Answer: The polar form of the rectangular equation $x = 4$is $\Rightarrow r = \dfrac{4}{{\cos \theta }}$.

Note:
Iif $(r,\theta )\;$ is a polar coordinate is given, substitute $r$ and $\theta$ into the equation for $x = r\cos \theta \;$ and $y = r\sin \theta \;$ to get $(x,y).$
The same holds true for if you are given an $(x,y)$ a rectangular coordinate instead.
To convert from polar to rectangular:
$x = r\cos \theta \;$
$y = r\sin \theta \;$
To convert from rectangular to polar:
${r^2} = {x^2} + {y^2}$
$\tan \theta = \dfrac{y}{x}$