anonymous
  • anonymous
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?
Mathematics
chestercat
  • chestercat
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dumbcow
  • dumbcow
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
  • anonymous
Thank you! That makes sense now. :D
dumbcow
  • dumbcow
yw :)

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anonymous
  • anonymous
Oops! One last thing. How did you get -x/y for the tangent line?
anonymous
  • anonymous
dumbcow
  • dumbcow
taking the derivative of circle equation and solving for "dy/dx"
anonymous
  • anonymous
Oh, sorry. Never mind. I think I figured it out.
anonymous
  • anonymous
Thank you. :)

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