What is a fixed sum of distances in an ellipse?

Question

for example, an ellipse has a fixed sum of distances equal to 12

Answer 1

1 .Draw an ellipse.
2. Draw the two foci (focus-es)
3. Draw a line (segment) from one focus to any point on the ellipse (call it Point A) then from that point (A) to the other focus. You'll have two line segments.

The sum of the length of these two segments is the same as the sum of the length of two segments using any other point, let's say a Point B.

This is the mathematical definition of ellipse.

Answer 2

Any point on the ellipse you described would be distance x from the first focus, and distance 12-x from the second focus. The sum of distances to the foci always equals 12 from any point on it. If you have an ellipse-shaped bowl of water, and you drop a pebble at one focus, all the waves created reach the other focus simultaneously because they all travelled the same distance (12 in your case).

Answer 3

It means that for any point on the ellipse, if you draw a segment connecting that point to each of the two foci and then add the two up--that number stays constant.

Answer 4

2a=12
a=6