4

Let's have the parabola $$ 4ay = x^{2}. $$ It rolls along the x-axis. How to prove that it's focus moves along the trajectory of the catenary, $$ y = a\cdot ch \left(\frac{x}{a}\right)? $$

John Taylor
  • 1,755
  • 11
  • 18
  • Unfortunately, I even don't know how to begin to solve this task. – John Taylor Feb 18 '13 at 19:47
  • Since the curve is rolling along the $x$-axis, I would start by finding the coordinates of the point on the original parabola that touches the $x$-axis at $(c,0)$. This will involve understanding the arc-length of segments of the parabola. – Greg Martin Feb 18 '13 at 19:52

0 Answers0