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. |

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. |

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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