How do you find the polar equation to graph of $x = 7$ ?

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Answer 1 · 2018-04-01T09:13:51

Substitute $x = rcos(theta)$ , then solve for $r$ as a function of $theta$ .

Given: $x = 7$

The following is a graph of the vertical line $x = 7$ :

![www.desmos.com/calculator]( useruploads.socratic.org )

Substitute $x = rcos(theta)$ :

$rcos(theta) = 7$

Divide both sides by $cos(theta)$ :

$r = 7/cos(theta)$

Substitute $sec(theta) = 1/cos(theta)$ :

$r = 7sec(theta)$

The conversion to polar form is done.

The following is a graph of $r = 7sec(theta)$ :

![www.desmos.com/calculator]( useruploads.socratic.org )

Please observe that the two graphs are identical.

How do you find the polar equation to graph of x = 7x = 7?