How precisely do you draw an oval that is exactly 3 feet by 4 feet using two nails, loop of string & a pencil?

I need to cut an oval out of plywood with these dimensions. I'd like to know if there's way to determine where the two nails would be placed and how long the string would be. Thanks a lot!How precisely do you draw an oval that is exactly 3 feet by 4 feet using two nails, loop of string %26amp; a pencil?
hi bob!


Do you mean ellipse? If so then its equation is: (x/a)^2+(y/b)^2=1, a=4, b=3;


Hammer nails in ellipse focuses with coordinates [-f 0] %26amp; [+f 0], now attach the rope ends to these nails, let the rope length be L, keep the rope taught with pencil and draw.


Let y=0, then x=a (or x=-a which does not matter here), then L=(a+f)+(a-f)=2*a


Let x=0, then y=b, then f^2+b^2=(L/2)^2, f=sqrt(a*2-b^2)How precisely do you draw an oval that is exactly 3 feet by 4 feet using two nails, loop of string %26amp; a pencil?
I forgot exactly, but I remember seeing it in a woodworking website, try free woodworking plans, you will have to filter thru a few pages but its out there.


Good luck.