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

Ernstfalld

Ernstfalld

Answered question

2021-09-22

Replace the Cartesian equation with equivalent polar equations.
(x+2)2+(y5)2=16

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-09-23Added 97 answers

Step 1
Given:
The Cartesian equation:
(x+2)2+(y5)2=16
Step 2
To convert into the polar equation, put
x=rcos0
y=rsin0
Therefore,
(x+2)2+(y5)2=16
(rcos0+2)2+(rsin05)2=16
Expand using:
(ab)2=a22ab+b2
(a+b)2=a2+2ab+b2
cos20+sin20=1
(r2cos20+2×rcos0×2+22)+(r2sin202×rsin0×5+52)=16
r2cos20+4rcos0+4+r2sin2010rsin0+25=16
r2(cos20+sin20)+4rcos010rsin0+13=0
r2+4rcos010rsin0+13=0
Thus,
The equivalent polar equation is:
r2+4rcos010rsin0+13=0
Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-27Added 2605 answers

Answer is given below (on video)

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