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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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