I guess the answer is the formula of focal radius: | pf1| = a+e * x0; (A is the semi-major axis and E is the eccentricity)

Formula pushdown uses the second definition of ellipse:

The distance from point p to the left directrix is x0+a2/c.

The second definition of ellipse is | pf1| = (x0+a 2/c) * e = a+e * x0;

In this problem, a= 10, b=6, c=8, e = 4/5;

So there is 10+4*(x0)/5= 15, and the solution is: x0 = 25/4;