For this problem, we are given the characteristics of an ellipse, and we need to determine its expression.
The general expression for an ellipse is given below:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Where (h,k) are the coordinates of the center, a is the major radius and b is the minor radius.
We are given the length of the major axis, we need to divide it by 2 in order to find the major radius:
[tex]a=\frac{8}{2}=4[/tex]
Then we are given the endpoint for the minor axis, which is (4, -1). Since this is aligned with the center at (4,0) we can determine the minor radius by subtracting the y-coordinates:
[tex]b=0-(-1)=1[/tex]
The ellipse's expression is:
[tex]\frac{(x-4)^2}{16}+y^2=1[/tex]
