## 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

1. kc_kennylau

Have you learnt differentiation yet?

2. Owlcoffee

You can try the polar line of the elipse, then consider the family of lines on the desired point with the conditions given.

3. anonymous

My notes; http://i.imgur.com/czFgEuq.png (finding tangent) http://i.imgur.com/rBAISmO.png (finding normal)

4. anonymous

first find the parametric equations for the ellipse x = h + a cos t y = k + b sin t

5. anonymous

Already got the parametric equation for the equation; http://i.imgur.com/73ELALw.png

6. anonymous

wouldn't it be part a) (-2, -2) + t * r ' (-2,-2) part b) (-2, -2) + t * -1 / r ' (-2,-2)

7. anonymous

r'(-2,-2) is [0, -1] Where can I find the formula/explaination for the b part you suggested, jazzdd?

8. anonymous

nevermind, we have to find t such that it comes to that point.

9. anonymous

to get to the point (-2,-2) we need t = π

10. anonymous

part a) (-2, -2) + t * r ' (π) part b) (-2, -2) + t * -1 / r ' (π)

11. anonymous

I think I already wrote that in the notes

12. anonymous

But I do not understand the part b) formula - where is it from, how did you conclude it

13. anonymous

the slope of the normal is perpendicular to the tangent line

14. anonymous

So I just multiply by -1 and divide by r'(..) to get any normal?

15. anonymous

for two dimensions, yes. for higher dimensions you have to use that formula N = T ' (t) / | T ' (t) |

16. anonymous

remember from algebra to find the slope of a perpendicular line, we use inverse reciprocal of the given line's slope

17. anonymous

I need to polish on old math (been forever since using them). I had trouble finding examples for two dimensions

18. anonymous

How would you write part b as an answer? $r(t_0)-t*r'(t_0)^{-1} ?$ (t_0 being pi)

19. anonymous

this is only valid in 2 dimensions finding a normal in 3 dimension is more involved

20. anonymous

yes r(t_0) + -1/ r ' (t _0) * t

21. anonymous

I 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

22. anonymous

so t is also underneath - divided?

23. anonymous

$[-2, -2] - \frac{ 1 }{ t*[0, -1] }$ ? Am I understanding it right?

24. anonymous

yes that is correct