Page 11 - ePC154_新一代技術高中數學C第四冊學習講義_課本PDF

Chapter 2 二次曲線 37

老師導引 範例 1 解析 P.22 學生演練

2
2
༊Ӌסيᇞ x + 4x - 8y + 12 = 0 ٙ௟ᓃމ ༊Ӌסيᇞ y - 8x - 4y - 4 = 0 ٙ௟ᓃމ
(-2 , 1) eೊᓃމ (-2 , 3) ၾ͍ೊָ (-1 , 2) eೊᓃމ (1 , 2) ၾ͍ೊָ
ڗމ 8 f ڗމ 8 f

2
Tips 答 ਗ਼ y - 8x - 4y - 4 = 0 ୅ධৣ˙
2
判斷類型 & 畫出簡圖 & 求出 h、k、c & 再代入標 ੻ y - 4y + 4 = 8x + 4 + 4
2
準式或相關元素公式 ݂੻ ( y - 2) = 4 × 2 × (x + 1)
ה˸௟ᓃ (h , k) = (-1 , 2) ˲ c = 2
2
答 ਗ਼ x + 4x - 8y + 12 = 0 ೊᓃމ (h + c , k) = (1 , 2)
୅ධৣ˙ ͍ೊָڗ 4|c| = 8
2
੻ x + 4x + 4
= 8y - 12 + 4

݂੻ (x + 2) 2
= 8y - 8

͵у (x + 2) 2
= 4 × 2 × ( y - 1)
ה˸௟ᓃމ (h , k) = (-2 , 1)d˲ c = 2dྡ
ҖකɹΣɪdೊᓃމ (h , k + c) = (-2 , 3)
͍ೊָڗ 4|c| = 8

老師導引 範例 2 解析 P.22 學生演練

2
2
༊Ӌסيᇞ y + 4x + 2y - 7 = 0 ٙೊᓃމ Ӌסيᇞ x - 6x - 8y - 23 = 0 ٙೊᓃމ
(1 , -1) e๟ᇞމ x = 3 ၾ࿁၈ൿ (3 , -2) e๟ᇞމ y = -6 ၾ࿁၈ൿ

މ y = -1 f މ x = 3 f
2
Tips 答 ਗ਼ x - 6x - 8y - 23 = 0 ୅ධৣ˙
2
判斷類型 & 畫出簡圖 & 求出 h、k、c & 再代入標 ੻ x - 6x + 9 = 8y + 23 + 9
2
準式或相關元素公式 ݂੻ (x - 3) = 4 × 2 × ( y + 4)
ה˸௟ᓃ (h , k) = (3 , -4) ˲ c = 2

2
答 ਗ਼ y + 4x + 2y - 7 = 0 ೊᓃމ (h , k + c) = (3 , -2)
୅ධৣ˙ ๟ᇞމ y = k - cdу y = -6
2
੻ y + 2y + 1 ࿁၈ൿމ x = hdу x = 3
= -4x + 7 + 1
݂੻ ( y + 1) 2
= -4x + 8
͵у
( y + 1) 2
= 4 × (-1) × (x - 2)
݂੻௟ᓃމ (h , k) = (2 , -1)d˲ c = -1
ྡҖකɹΣ̸dೊᓃމ (h + c , k) = (1 , -1)
๟ᇞމ x = h - cdу x = 3
࿁၈ൿމ y = kdу y = -1