Identify the curve by finding a Cartesian equation for the curve. r=2\cos \th

nitraiddQ

nitraiddQ

Answered question

2021-09-22

Identify the curve by finding a Cartesian equation for the curve. r=2cosθ

Answer & Explanation

Clara Reese

Clara Reese

Skilled2021-09-23Added 120 answers

The polar coordinates are related to the Cartesian coordinates by the equations:
r2=x2+y2   x=rcosθ   y=rsinθ
We change from polar to Cartesian by substituting as needed.
r=2cosθ
r2=2rcosθ multiply both sides by r
(x2+y2)=2(x) substitute
x22x+y2=0 get x terms to one side
(x22x+1)+y2=1 complete the square: +1 to both sides
(x1)2+y2=1
Now in the standard circle form of (xh)2+(yk)2=r2 we see that we have a circle of radius r=1
centered at (h,k)=(1,0)
Result:
circle centered at (1,0), radius =1

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