Question

已知圆C:x^2+y^2+2x-4y+3=0.求z=y+1/x+1的取值范围

Answer 1

C: x^2+y^2+2x-4y+3 = 0 即 (x+1)^2 + (y-2)^2 = 2

令 x = -1 + √2 cost, y = 2 + √2 sint

z = (y+1) / (x+1) = ( 3 + √2 sint ) / (√2 cost)

z = y + 1/x + 1 = 3 + √2 sint + 1/ (-1+√2 cost)