問一題大學數學..題目看不懂..

[阿銘 10]

An asteroid has an equation of the form x^2/3+y^2/3=a^2/3 , where a is a positive constant. Find dy/dx and show that the length of the portion of any tangent line to the asteroid cut off by the coordinate axes is constant.

題目如上..有人能幫忙翻譯一下順便解題嗎?

感恩

[Morris 10]

我翻譯看看.....這應該是微積分吧qq

一個有 x^2/3+y^2/3=a^2/3 型式的星芒線方程，a 是一個正的常數

求dy/dx，以及證明星芒線切線被座標軸擷取部份的長度為常數

題目翻完後，解題就不難了XD

此內容已被編輯, July 30, 2010 ,由 Morris

[djshen1217 10]

好像是問切線被座標軸所截長度=定值

dy/dx=-(x/y)^(-1/3)

設切點為(p,q)

符合p^(2/3)+q^(2/3)=a^(2/3)

切線方程式

y-q

----- = -(p/q)^(-1/3)

x-p

得x截距=p+p^(1/3)q^(2/3)

y截距=q+p^(2/3)q^(1/3)

被座標軸截的長度^2=x截距^2+y截距^2=p^2+3p^(4/3)q^(2/3)+3p^(2/3)q(4/3)+q^2=(p^(2/3)+q^(2/3))^3=a^2

所求=a

用高中方法解的

此內容已被編輯, July 31, 2010 ,由 djshen1217

[阿銘 10]

謝謝你們 問題已解決

[Mr.clever 10]

這題應該是要用Implicit differentiation