9.04 Ellipses

Consider the following ellipse. The points given are the foci of the ellipse. Find the value of $x$x.

Mario picks out a piece of string $8$8 inches long. He fixes each end of the string at points $F$F and $G$G on a chalkboard as shown, such that $F$F and $G$G are $6$6 inches apart and equidistant to point $O$O. He pulls the string taut and then uses chalk to trace out the curve shown below.

Let $A$A and $B$B be the foci of an ellipse. $C$C and $D$D are points on the ellipse. Write an equation showing the relation between the lengths of the segments, $AB$AB, $AD$AD, $BC$BC and $BD$BD.