曲线的所有主法线通过某个固定点
=>曲线的所有切线与某个固定点垂直
设固定点(x0,y0),
曲线 ; y= f(x)
[(y-y0)/(x-x0)] . f'(x) =-1
(x-x0)dx = (y-y0) dy
(x-x0)^2/2+(y-y0)^2/ 2 = C'
(x-x0)^2+(y-y0)^2 = 2C'
= C ( C=2C')
equation of circle 曲线的所有主法线通过某个固定点
=>曲线的所有切线与某个固定点垂直
设固定点(x0,y0),
曲线 ; y= f(x)
[(y-y0)/(x-x0)] . f'(x) =-1
(x-x0)dx = (y-y0) dy
(x-x0)^2/2+(y-y0)^2/ 2 = C'
(x-x0)^2+(y-y0)^2 = 2C'
= C ( C=2C')
equation of circle