I'm asked to calculate the curvature of an ellipse:
(x^2/a^2)+(y^2/b^2)=1
The professor is setting x(t) = acos(t) and y(t) = bsin(t)
but I don't know why.
I think I can calculate the curvature from there.
Any help is appreciated.
I'm asked to calculate the curvature of an ellipse:
(x^2/a^2)+(y^2/b^2)=1
The professor is setting x(t) = acos(t) and y(t) = bsin(t)
but I don't know why.
I think I can calculate the curvature from there.
Any help is appreciated.
The empty set made a couple of small mistakes reducing the parameteric equation. I'm a newbie here, so I may get the markup wrong, but:
which, because , simplifies to:
Test: if a = b = r for a circle,
For a circle, the curvature becomes 1/r as expected.
Thank you "Mr. Set" for showing me how to solve this, and an opportunity to help.