设x-2=cosθ,y+3=sinθ.
①x+y=(2+cosθ)+(-3+sinθ)
=-1+√2sin(θ+π/4).
sin(θ+π/4)=1时,
所求最大值为:-1+√2;
sin(θ+π/4)=-1时,
所求最小值为:-1-√2.
②√(x²+y²+2x-4y+5)
=√[(x+1)²+(y-2)²]
=√[(3+cosθ)²+(-5+sinθ)²]
=√[35+2√34cos(θ+φ)]
(其中,tanφ=-5/3)
∴cos(θ+φ)=1时,所求最大值:
√(35+2√34)=√34+1;
cos(θ+φ)=-1时,所求最小值:
√(35-2√34)=√34-1.