玲我爱你
幼苗
共回答了17个问题采纳率:94.1% 举报
推导x^2=2py:
设点M(x,y)到直线y=-p/2的距离,和到点F(0,p/2)的距离相等.
点M(x,y)到直线y=-p/2的距离=[y+p/2],[MF]=根号[x^2+(y-p/2)^2].
[y+p/2]^2=x^2+(y-p/2)^2 y^2+py+p^2/4=x^2+y^2-py+p^2/4 x^2=2py
推导x^2=-2py:
设点M(x,y)到直线y=p/2的距离,和到点F(0,-p/2)的距离相等.
点M(x,y)到直线y=p/2的距离=[y-p/2],[MF]=根号[x^2+(y+p/2)^2].
[y-p/2]^2=x^2+(y+p/2)^2 y^2-py+p^2/4=x^2+y^2+py+p^2/4 x^2=-2py
1年前
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