# Search results

1. ### Find the curve with the shortest path on a surface (geodesic)

Homework Statement Let ##U## be a plane given by ##\frac{x^2}{2}-z=0## Find the curve with the shortest path on ##U## between the points ##A(-1,0,\frac{1}{2})## and ##B(1,1,\frac{1}{2})## I have a question regarding the answer we got in class. Homework Equations Euler-Lagrange ##L(y)=\int...
2. ### Finding the parametric equation of a curve

Thank you I was able to find the solutin once I saw the video
3. ### Finding the parametric equation of a curve

Homework Statement Parameterize the part of the curve which allows an equilateral triangle, with the height 3R, to roll from one vertex to the next one, while its center travels at a constant height. Homework Equations I will include some pictures to show what I'm doing The Attempt at a...
4. ### Finding Orthogonal Trajectories (differential equations)

Homework Statement Find Orthogonal Trajectories of ##\frac{x^2}{a}-\frac{y^2}{a-1}=1## Hint Substitute a new independent variable w ##x^2=w## and an new dependent variable z ##y^2=z## Homework Equations The Attempt at a Solution substituting ##x## and ##y## I get...