ellipse - Turing のブログ

ellipse　

　 ${\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1$ 　

$∠$ $F_{1}$

$P$

( -√b²-a²±2√b²-a²-(1- $b 2 / a 2$ )/(1- $b 2 / a 2$ )，± b√(1-｛-√b²-a²±2√b²-a²-(1- $b 2 / a 2$ )/(1- $b 2 / a 2$ )} ² / a² )

$∠$ $APB = 90°$

$| AP | = \sqrt( a+\sqrt2a 2 -b 2 / 3 - b 2 / a 2$ ) $2$ + b² {1-(√2a²-b² / 3 - $b 2 / a 2$ )² / a²}

$|$ $BP$ $| =\sqrt ( a-\sqrt2a 2 -b 2 / 3 - b 2 / a 2) 2 + b 2 {1-(\sqrt2a 2 -b 2 / 3 - b 2 / a 2) 2 / a 2}$

( √2a²-b² / 3 - $b 2 / a 2$ ，± b√1-(√2a²-b² / 3 - $b 2 / a 2$ )² / a²)

( √2a²-b² / 3 - $b 2 / a 2$ -2a，± b√1-(√2a²-b² / 3 - $b 2 / a 2$ )² / a²)

　T.theodor 2022.7.26