How do you convert the rectangular equation 5x+7y=125x+7y=12 into polar form?

1 Answer
Douglas K.
Jan 9, 2017

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

Explanation:

Here is a graph of the given equation:

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

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

5rcos(theta) + 7rsin(theta) = 125rcos(θ)+7rsin(θ)=12

Factor out r:

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

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

r = 12/(5cos(theta) + 7sin(theta))r=125cos(θ)+7sin(θ)

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

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