作业帮show that every normal to the curve y=根号（A的平方-X的平方）will always pass through the point (0,0).
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show that every normal to the curve y=根号（A的平方-X的平方）will always pass through the point (0,0).
show that every normal to the curve y=根号（A的平方-X的平方）will always pass through the point (0,0).
show that every normal to the curve y=根号（A的平方-X的平方）will always pass through the point (0,0).
normal 的意思是法线,即垂直于切线的过切点的直线.
y=√(a^2-x^2)
求导：
y\'|x=x0=-x0/√(a^2-x0^2)
这是切线斜率,法线斜率为：
m1=-1/m=√(a^2-x0^2)/x0
带入点斜式方程：
y-√(a^2-x0^2)=√(a^2-x0^2)/x0*(x-x0)
带入x=0,化简可得y=0
∴every normal to the curve will always pass through (0,0).
还可以从几何角度考虑,这是一个半圆,圆心在原点,半径为a.
初中几何里就有相关定理可证明法线为过切点的直径,所以经过原点.
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