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anonymous
 one year ago
How do I find the normal and tangent equations?
x^2/4 + (y+2)^2 = 1 (ellipse)
"Find the parametrized equation to the tangent and normal in point (2, 2)."
I believe the tangent is [2, 2] + t[0, 1] (although I am not sure),
and I believe the normal is [2, 2] + t[1, 0] (How do you get to the solution? I just "saw" it, but I cant figure out how to mathematically do it!)
Tried N = N(vector) / N(scalar), but .. nope
anonymous
 one year ago
How do I find the normal and tangent equations? x^2/4 + (y+2)^2 = 1 (ellipse) "Find the parametrized equation to the tangent and normal in point (2, 2)." I believe the tangent is [2, 2] + t[0, 1] (although I am not sure), and I believe the normal is [2, 2] + t[1, 0] (How do you get to the solution? I just "saw" it, but I cant figure out how to mathematically do it!) Tried N = N(vector) / N(scalar), but .. nope

This Question is Closed

kc_kennylau
 one year ago
Best ResponseYou've already chosen the best response.0Have you learnt differentiation yet?

Owlcoffee
 one year ago
Best ResponseYou've already chosen the best response.0You can try the polar line of the elipse, then consider the family of lines on the desired point with the conditions given.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My notes; http://i.imgur.com/czFgEuq.png (finding tangent) http://i.imgur.com/rBAISmO.png (finding normal)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first find the parametric equations for the ellipse x = h + a cos t y = k + b sin t

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Already got the parametric equation for the equation; http://i.imgur.com/73ELALw.png

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldn't it be part a) (2, 2) + t * r ' (2,2) part b) (2, 2) + t * 1 / r ' (2,2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0r'(2,2) is [0, 1] Where can I find the formula/explaination for the b part you suggested, jazzdd?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0nevermind, we have to find t such that it comes to that point.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0to get to the point (2,2) we need t = π

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0part a) (2, 2) + t * r ' (π) part b) (2, 2) + t * 1 / r ' (π)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I already wrote that in the notes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0But I do not understand the part b) formula  where is it from, how did you conclude it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the slope of the normal is perpendicular to the tangent line

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I just multiply by 1 and divide by r'(..) to get any normal?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for two dimensions, yes. for higher dimensions you have to use that formula N = T ' (t) /  T ' (t) 

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0remember from algebra to find the slope of a perpendicular line, we use inverse reciprocal of the given line's slope

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I need to polish on old math (been forever since using them). I had trouble finding examples for two dimensions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How would you write part b as an answer? \[r(t_0)t*r'(t_0)^{1} ?\] (t_0 being pi)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is only valid in 2 dimensions finding a normal in 3 dimension is more involved

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes r(t_0) + 1/ r ' (t _0) * t

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand  I have found tons of material on "planes"  not what I wanted for this task , had to find the "simple" 2D plane normals, I just dont remember much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so t is also underneath  divided?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[[2, 2]  \frac{ 1 }{ t*[0, 1] }\] ? Am I understanding it right?
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