已知圆的极坐标方程为p^2-4√2pcos(θ-π/4)+6=0,

(1) p² - 4√2pcos(θ-π/4) + 6 = 0
p² - 4√2p [cosθcos(π/4) + sinθsin(π/4)] + 6 = 0 (利用两角差的馀弦公式)
p² - 4√2p [cosθ (1/√2) + sinθ (1/√2)] + 6 = 0
p² - 4pcosθ - 4psinθ + 6 = 0
x² + y² - 4x - 4y + 6 = 0 (x = pcosθ,y = psinθ,x² + y² = p²)
(x - 2)² + (y - 2)² = 2
(2) 设圆的参数方程为 x = 2 + √2cosα,y = 2 + √2sinα (设α是为免与(1)式中的θ混为一谈)
则 x + y = 2+ √2cosα + 2 + √2sinα
= 4 + √2(cosα + sinα)
= 4 + √2 * √2 [cosα (1/√2) + sinα (1/√2)]
= 4 + 2 [cosα sin(π/4) + sinα cos(π/4)]
= 4 + 2sin(α + π/4) (利用两角和的正弦公式)
当sin(α + π/4) = 1时,x + y 有最大值为6
当sin(α + π/4) = -1时,x + y 有最小值为2