Replace the Cartesian equation with equivalent polar equations. x^{2}+(y-2)^{2}=4

chillywilly12a

chillywilly12a

Answered question

2021-05-16

Replace the Cartesian equation with equivalent polar equations.
x2+(y2)2=4

Answer & Explanation

Caren

Caren

Skilled2021-05-17Added 96 answers

Step 1 
Given: 
The Cartesian equation 
x2+(y2)2=4 
Step 2 
To construct the polar equation, use:
x=rcos0 
y=rsin0 
Thus, 
x2+(y2)2=4 
(rcos0)2+(rsin02)2=4 
r2cos20+r2sin202×rsin0×2+22=4   [(ab)2=a22ab+b2] 
r2(cos20+sin20)4rsin0+4=4 
r24rsin0=0   [cos20+sin20=1] 
Thus, 
The polar equation that is equivalent is:
r24rsin0=0

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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