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±×¸²°ú °°ÀÌ Å¸¿ø À§ÀÇ ÇÑÁ¡ P ¸¦ Æ÷ÇÔÇÏ°í x, y Ãà¿¡ ÆòÇàÇÑ Á÷»ç°¢ÇüÀÇ ÃÖ´ë ¸éÀûÀ» ±¸ÇÑ´Ù.

Ÿ¿øÀÇ ¹æÁ¤½ÄÀº ´ÙÀ½°ú °°´Ù.

x^2/a^2 + y^2/b^2 = 1

»ï°¢Ä¡È¯À» ÀÌ¿ëÇϸé, Á¡ PÀÇ ÁÂÇ¥´Â (a*cos¥è, b*sin¥è) °¡ µÇ¹Ç·Î, Ÿ¿ø¿¡ ³»Á¢ÇÏ´Â Á÷»ç°¢ÇüÀÇ ¸éÀûÀº

A = 4*x*y = 4*a*b*cos¥è*sin¥è

ÀÌ µÈ´Ù. ¿©±â¼­, 2*cos¥è*sin¥è = sin(2¥è) À̹ǷÎ,

A = 2*a*b*sin(2¥è)

°¡ µÇ°í sin(2¥è)¡Â1 À̹ǷÎ,

Amax = 2*a*b

°¡ µÈ´Ù.

*** Âü°í¹®Çå[References] ***

Amax = 2*a*b
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