駭客數學(圓與圓錐曲線)

[j2e037]

1.一曲線任一點之座標(x,y),滿足x=(tan t/2)+2,y=2/(cot+1),t為實數,則下列何者不正確?
(A)圖形與y軸交於點(0,5)
(B)圖形之最低點為(2,1)
(C)x^2-4x-y=0
(D)圖形為一拋物線
Ans:(C)

請老師幫忙解惑!謝謝^^

[thepiano]

x = tan(t/2) + 2
y = 2 / (cost + 1)

(x - 2)^2 = [tan(t/2)]^2 = (1 - cost) / (1 + cost)
(x - 2)^2 + 1 = (1 - cost) / (1 + cost) + 1 = 2 / (1 + cost) = y

y = (x - 2)^2 + 1