https://www.mathopenref.com/ellipse.html
Look at the first ellipse picture on the site. The point on the ellipse moves with the mouse. Notice the line a is from one point in the middle line. Just think of one brad nail being point a, the line a is going to be the string from that brad nail to the outside of the circle. The line b is the string from the other brad nail, point b. When you move the outer string point, less say a to the line that goes through the two brad nails, you get the outer point. That going to be the outer end of the ellipse left of brad a. Move the string point to the line that goes through the brads, say b and go to the right side you get the end of the ellipse from brad nail b. Move the point around the ellipse and remember, point a is a brad nail, point b is a brad nail. The line a is the length the string will reach to the ellipse from nail a. The line b is the string that will reach the ellipse from nail b.
Play with the picture, that grab some cardboard, two brad nails and different loops of string, As you move the brad nails closer and further from each other your going to see the ellipse flatten and expand. The string loop will always be the same until you make a different size. A whole group of string loops and you can make an ellipse on the living room floor with the right length. RJF