運(yùn)用圓的參數(shù)方程
P(cosa-2,sina)0<=a<2π
（1）點(diǎn)P到直線的距離=|3cosa-6+4sina+12|/5
=|5sin(a+arccos(4/5))+6|/5
最小值為1/5,最大值為11/5
（2）x+y=cosa+sina-2
=√2sin(a+π/4)-2
最大值為√2-2,最小值為-√2-2
（3）(y-2)/(x-1)=(sina-2)/(cosa-3)
令t=tan(a/2)sina=2t/(1+t^2)cosa=(1-t^2)/(1+t^2)
(y-2)/(x-1)=(2t-2-2t^2)/(1-t^2-3-3t^2)
=(t^2-t+1)/(2t^2+1)
=1/2*(t^2+1/2-t+1/2)/(t^2+1/2)
=1/2*[1-(t-1/2)/(t^2+1/2)]
=1/2-1/2*(t-1/2)/[(t-1/2)^2+(t-1/2)+3/4]
=1/2-1/2*1/[(t-1/2)+3/4*1/(t-1/2)+1]
最小值為(3-√3)/4,最大值為(3+√3)/4
當(dāng)且僅當(dāng)t=(√3+1)/2和(1-√3)/2時(shí),等號成立