partial differentiation3

http://img222.imageshack.us/img222/1797/18762758.png

圖片參考：http://img222.imageshack.us/img222/1797/18762758.png

Let the point (b,c) be a point on x^2 + y^2 = a^2.

d(x^2 + y^2)/dx = d(a^2)/dx
2x + 2y dy/dx = 0
2y dy/dx = -2x
dy/dx = -2x/2y
= -x/y

Slope of tangent on point (b,c) = -b/c
Slope of normal on point (b,c) = -1 / (-b/c) = c/b

The equation of the normal on (b,c) is given as:
y - c = c/b (x - b)
b (y - c) = c (x - b)
by - bc = cx - bc
by = cx
y = c/b x

Also note that the normal always passes the origin for any points on the circle.
We may just get the equation by y = (slope of normal) x, i.e. y = c/b x