Last question! YAY!
How can I show that the normal line at any point on the circle x^2 + y^2 = r^2 passes through the origin?

Question

Last question! YAY!
How can I show that the normal line at any point on the circle  x^2 + y^2 = r^2  passes through the origin?

dumbcow · Answer

first show that slope of tangent line is dy/dx
$$\frac{dy}{dx} = -\frac{x}{y}$$
slope of normal is opp reciprocal
$$m = \frac{y}{x}$$
next use equation of normal line to show y-intercept is 0
$$y - y_0 = m(x - x_0)$$
$$y = mx + (y_0 - mx_0)$$
$$y = mx + (y_0 - \frac{y_0}{x_0} x_0) = mx$$
Since y-intercept is 0, every normal line must go through origin

anonymous · Answer

Thank you! That makes sense now. :D

dumbcow · Answer

yw :)

anonymous · Answer

Oops! One last thing. How did you get  -x/y  for the tangent line?

anonymous · Answer

@dumbcow

dumbcow · Answer

taking the derivative of circle equation and solving for "dy/dx"

anonymous · Answer

Oh, sorry. Never mind. I think I figured it out.

anonymous · Answer

Thank you. :)