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# What is the rectangular form of 𝑟^2=4𝑟sin𝜃+5

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Hello can i get some help on how to transform this equation from a polar coordinate system to a rectangular coordinate system step by step please

r2=4rsin𝜃+5

May 27, 2021

#1
+26321
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Hello can i get some help on how to transform
this equation from a polar coordinate system
to a rectangular coordinate system

$$r^2=4r\sin(\theta)+5$$

Formula:
$$\boxed{\sin(\theta)=\dfrac{y}{r}~ \text{or}~ y=r\sin(\theta)\\ r = \sqrt{x^2+y^2}}$$

$$\begin{array}{|rcll|} \hline r^2 &=& 4r\sin(\theta)+5 \\ x^2+y^2 &=& 4y+5 \\ \mathbf{x^2+y^2-4y-5} &=& \mathbf{0} \\ \hline \end{array}$$

May 27, 2021