The equivalent polar equation for the given rectangular-coordinate equation: x^{2} + y^{2} + 8x=0

allhvasstH 2020-12-24 Answered
The equivalent polar equation for the given rectangular-coordinate equation:
x2 + y2 + 8x=0
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Expert Answer

Asma Vang
Answered 2020-12-25 Author has 93 answers

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
Converting into equivalent polar coordinates:
[x2 + y2 + 8x=0
Put x=rcosθ, y=rsinθ,
 (rcosθ)2 + (rsinθ)2 + 8rcosθ=0
 r2cos2θ + r2sin2θ + 8rcosθ=0
 r2 (cos2θ +sin2 θ) + 8rcosθ=0
{cos2θ +sin2 θ=0}
 r2 + 8rcosθ=0
 r + 8cosθ=0
Hence, desired equivalent polar coordinates would be r + 8cosθ=0

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