Question

Find the curvature at the point (x, y) on the ellipse x^2/9+y^2/4=1.

Answer 1

\[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]

Answer 2

So I know that a=3 and b=2 for this problem, and x(t)=3cos(t) and y(t)=2sin(t). But now what do I do? What's the formula for finding the curvature for this problem?

Answer 3

@Loser66 @Zarkon @iambatman @freckles @Hero @dan815 @paki

Answer 4

http://tutorial.math.lamar.edu/Classes/CalcIII/Curvature.aspx

you'll find a few worked examples here .....

Answer 5

https://answers.yahoo.com/question/index?qid=20150330125959AA4apUS

Answer 6

Curvature: \[\kappa =\left|\frac{\vec T'(t)}{\vec r'(t)}\right| \]\[r(t) = \langle 3\cos(t)~,~2\sin(t)\rangle\]\[T(t) = \frac{r(t)}{|r'(t)|}\]

Answer 7

solve for all those, plug it in, you'll find your answer.

Answer 8

SOrry I made a typo.

Answer 9

\[T(t) = \frac{r'(t)}{|r'(t)|}\]

Answer 10

Oh and the other form of curvature is: \[\kappa = \frac{|\vec r'(t) \times \vec r''(t)|}{|r'(t)|^3}\]Whichever you find easier to do, really.

Answer 11

Thank you, it worked!

Answer 12

:) yay