Okay, So I'm Stuck On This One Problem...any Help...

PhdJay28

From: US
Posts: 4
Votes: 12
Okay, so I'm stuck on this one problem...any help isappreciated: Show that the normal line at any point on the circle x^2 + y^2 =r^2 passes through the origin. I have no idea how to even start this; the back of the book doesnot give the answer. The answer should be some kind of proof, but Iam having trouble understanding how to begin doing this. Pleasehelp! Thanks.

 

Answer No.1

Anonymous

From: -
Posts: -
Votes: -
X^2 + y^2 = r^2 so, 2x + 2ydy/dx = 0 so, dy/dx = -x'/y' at (x',y') = slopeof the tangent. so, slope of normal = -dx/dy = y'/x' so, equation of normal = y'/x' = (y - y')/(x -x') so, xy' - x'y' = x'y - x'y' so, xy' - yx' = 0 so, y = xy'/x' + 0 as y-intercept = 0, the normal passes through theorigin.

Answer No.2

MathGenius43

From: US
Posts: 7
Votes: 14
This question is exactly like one in our book that I did a whileback, but Yougotmath has it typed up already: /solution-player.aspx?solution_problem_id=160218

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