MATHS differentialtion

2010-12-30 2:50 am
諗左好耐都唔識計,唔該哂你地!!

find the point(s) on the parabola y=1/4x^2 which is/ are closest to the point (0,5)

更新1:

[(k-5)/h][h/2]=-1 不明白....那個-1是什麼?這是什麼式的?

更新2:

那個-1是不是 因為 line joining (0,5) and (h,k) 同條tangent 垂直,所以 slpoe of tangent(h/2) 乘 slope of line joining (0,5) and (h,k)=-1,是不是這樣?

回答 (1)

2010-12-30 3:59 am
✔ 最佳答案
y=(1/4)x^2 ; dy/dx=x/2. Let the point on the parabola which is closest to the point (0,5) is (h,k). Then the line joining (0,5) and (h,k) should be normal to the tangent line about (h,k). So [(k-5)/h][h/2]=-1 =>k=3 Then h=2√ 3 or
-2√ 3

So, the required points are (-2√ 3, 3) and (2√ 3,3)

2010-12-29 22:29:19 補充:
YES


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