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High score on ellipse problem in high school mathematics.
1, the focus is symmetrical, so the center of the circle is at the origin, and a vertex of the long axis is (5,0), then a=5,

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).