How do you convert the rectangular equation #5x+7y=12# into polar form?

Question

5322 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-09T19:47:04

Substitute #rcos(theta)# for x and #rsin(theta)# for y and then use algebra to express r as a function of #theta#, if possible.

Here is a graph of the given equation:

graph{5x + 7y = 12 [-10.33, 9.67, -5.32, 4.68]}

Substitute #rcos(theta)# for x and #rsin(theta)# for y:

#5rcos(theta) + 7rsin(theta) = 12#

Factor out r:

#r(5cos(theta) + 7sin(theta)) = 12#

Divide both sides by #(5cos(theta) + 7sin(theta))#

#r = 12/(5cos(theta) + 7sin(theta))#

Here is a graph of the polar equation:
enter image source here