How do you convert #3x - 2y= 6# into polar form?

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Answer 1 · 2015-11-24T05:17:00

#=> r = 6/(3cos(theta)-2sin(theta))#

When converting between polar and rectangular coordinates, we use the following equalities:
#{(x = rcos(theta)), (y = rsin(theta)):}#

Substituting these into the equation,

#3x - 2y = 6# becomes

#3rcos(theta) - 2rsin(theta) = 6#

#=> r(3cos(theta) - 2sin(theta)) = 6#

#=> r = 6/(3cos(theta)-2sin(theta))#