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.