The discussion revolves around finding the curvature at a specific point on the ellipse defined by the equation x²/9 + y²/4 = 1. Participants are exploring the mathematical principles related to curvature in the context of this ellipse.
The conversation is ongoing, with participants sharing their attempts and seeking clarification on the curvature concept. Some guidance has been offered regarding textbook resources, but no consensus has been reached on the approach to take.
There is a noted absence of specific equations for curvature in the original posts, and participants are navigating the need for a formula while discussing the parametric representation of the ellipse.
If you textbook has a problem about finding curvature, I can pretty much guaranteed that it will have a formula for curvature somewhere close by in the book. That should be the first place you look.Math10 said:Homework Statement
Find the curvature at the point (x, y) on the ellipse x^2/9+y^2/4=1.
Homework Equations
None.
The Attempt at a Solution
x^2/a^2+y^2/b^2=1
so I know that a=3 and b=2 for this problem.
x(t)=acos(t) and y(t)=bsin(t)
so x(t)=3cos(t) and y(t)=2sin(t)
now what? What's the formula for finding the curvature for this problem? The answer is 162/(81-5x^2)^(3/2).