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双曲線の接線・法線

著者:Mathcot

初版:2007.12.01

Update:2007.12.02



双曲線
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:






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