To find: The equivalent polar equation for the given rectangular-coordinate equation.Given:\displaystyle{x}^{2}+{y}^{2}+{8}{x}={0}

Kyran Hudson 2021-02-08 Answered

To find: The equivalent polar equation for the given rectangular-coordinate equation.
Given:
x2+y2+8x=0

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Expert Answer

faldduE
Answered 2021-02-09 Author has 109 answers

Concept used: Conversion formula for coordinate systems are given as
a)
From polar to rectangular:
x=rcosθ
y=rsinθ
b)
From rectangular to polar:
r=±x2+y2
cosθ=xr;sinθ=yr;tanθ=xy
Calculation:
Converting into equivalent polar equation
x2+y2+8x=0
Put {x}={r}cos{θ},{y}={r}sin{θ},
x=rcosθ,y=rsinθ
(rcosθ)2+(rsinθ)2+8rcosθ=0
r2cos2θ+r2sin2θ+8rcosθ=0
r2(cos2θ+sin2θ)+8rcosθ=0{cos2θ+sin2θ=1}
r2+8rcosθ=0
r+8cosθ=0
Thus, desired equivalent polar equation would be r+8cosθ=0

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