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anonymous
 one year ago
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?
anonymous
 one year ago
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?

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dumbcow
 one year ago
Best ResponseYou've already chosen the best response.1first 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 yintercept 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 yintercept is 0, every normal line must go through origin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you! That makes sense now. :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops! One last thing. How did you get x/y for the tangent line?

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.1taking the derivative of circle equation and solving for "dy/dx"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, sorry. Never mind. I think I figured it out.
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