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

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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

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