c=4,b=√(a^2-c^2)=3，
The elliptic equation is: x 2/25+y 2/9 =1.
2. Let the elliptic equation be y 2/b 2+x 2/a 2 =1,(b >；; a & gt0),
Substitute the coordinate values of two points (0,2) and (1, 0) into the equation respectively, which is exactly the coordinate values of two vertices.
The length of the long semi-axis is 2, and the length of the short semi-axis is 1.
So the elliptic equation is: y 2/4+x 2 =1.
3. Let the elliptic equation be: x 2/a 2+y 2/b 2 =1,let the focus be on the X axis, a>b>0,
Substitute the coordinate values of two points into the equation respectively,
3/a^2+ 1/4/b^2= 1,( 1)
15/4/a^2+ 1/ 16/b^2= 1,(2)，
(2)*4-( 1) formula,
a=2，
b= 1，
The equation is: x 2/4+y 2 = 1,
2> 1 So the focus is on the X axis, and the previous assumption is correct.
4 、|AB|+|AC|= 18-8= 10，
According to the definition of ellipse,
Obviously, the trajectory A is an ellipse, and B and C are the two focuses of the ellipse.
2a= 10，a=5，
2c=8，c=4，
b^2=a^2-c^2=9，
The elliptic equation is: x 2/25+y 2/9 =1,(y ≠ 0).