標準形 基準点(0, 0), 曲線上の点(xo,yo) |
基準点(p, q), 曲線上の点(xo,yo) |
(1) (x/a)^2 -(y/b)^2 = 1 漸近線:(x/a)^2 -(y/b)^2 =0 接線:xxo/a^2 -yyo/b^2 = 1 法線: |
(x-p)^2/a^2 -(y-q)^2/b^2 = 1 漸近線:(x-p)^2/a^2 -(y-q)^2/b^2 =0 接線:(x-p)(xo-p)/a^2 -(y-q)(yo-q)/b^2 = 1 法線: |
x^2/9-y^2/4 = 1 漸近線:x/3 = y/2, x/3 = -y/2 接線:4x/9 -y(√7)/12 = 1 (接点(4, (2/3)√7)) 法線: |
|
(2) (x/a)^2 -(y/b)^2 = -1 漸近線:(x/a)^2 -(y/b)^2 =0 接線:xxo/a^2 +yyo/b^2 = -1 法線: |
(x-p)^2/a^2 -(y-q)^2/b^2 = -1 漸近線:(x-p)^2/a^2 -(y-q)^2/b^2 =0 接線:(x-p)(xo-p)/a^2 -(y-q)(yo-q)/b^2 = -1 法線: |
(3) xy=k 漸近線:x=y=0 接線:xyxoyo=k^2 法線: |
(x-p)(y-q)=k 漸近線:x=p, y=q 接線:xxo/a^2 +yyo/b^2 = 1 法線: |