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# Polar Equation >> Rectangular Equation

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Convert $$r = {7 \over 9sinθ-cosθ}$$ to rectangular form.

Enter your answer in slope-intercept form by filling in the boxes. Enter values so that fractions are simplified.

$$y = { [] \over []} x + \frac{[]}{[]}$$

Hello:) I'm trying to convert the polar equation above into a rectangular equation. I looked up a Youtube video to do it and I got stuck after a certain point.

Here's my work:

1) I multiplied r on both sides.

$$r^2 = {7 \over 9sinθ - cosθ} \times r$$

2) Because r2 equals x2 + y2 , I substituted x2 + y2​ into r2.

$$x^2 + y^2= {7 \over 9sinθ-cosθ}\times r$$

For the next part, I'm confused, because it says that cosθr is equal to x. And because the r is being multiplied at the end, I'm tripped up lol so if someone could help me understand the next step, I'd appreciate that so much!

Jun 4, 2020

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I'm not sure about the approach you took, but have you tried multiplying both sides by the denominator($$9\sin{\theta}-\cos{\theta}$$) from the beginning? Maybe that would get you somewhere, since you know that $$r * \cos{\theta} = x$$ and $$r * \sin{\theta} = y$$

Not sure if you're asking for the solution, but if you are, then you can keep reading I guess.

Using the method mentioned above:

$$9r\sin{\theta} - r\cos{\theta} = 7$$

Using our substitutions, we rewrite this as:

$$9y - x = 7$$

From here on out, it gets pretty intuitive. Dividing and rearranging to get our desired form, we get:

$$9y = x+7$$

$$y = x/9 + 7/9$$

or

$$y = \frac19 x + \frac79$$

Hope this helped!

Jun 4, 2020
edited by jfan17  Jun 4, 2020
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Omigosh! I can see where I went wrong. I should've seen that lol. I understand 100% now. Thank you so so so much. You're a life savior!! Truly:)

auxiarc  Jun 4, 2020