Solution
The standard form for the ellipse whose major axis
Write the equation in a standard form
[tex]x^2-8x+25y^2-100y+91=0[/tex][tex]\begin{gathered} x^2-8x_+25y-100y+91=0 \\ x^2-8x+4^2+25y^2-100y=91 \\ (x-4)^2+25(y^2-4y)=91 \\ (x-4)^2+25(y-2)^2=91+16+25(4) \\ (x-4)^2+25(y-2)^2=116-91 \\ \frac{(x-4)^2+25(y-2)^2=25}{25} \\ \frac{(x-4)^2}{25}+\frac{(y-2)^2}{1}=1 \end{gathered}[/tex](1) The centre of the ellipse is (h , k)
[tex]h=4,k=2[/tex](2) The value of a = 5
(3) The value of b = 1
(4) The foci with the positive x value is the points
[tex](0,+5)[/tex](5) The foci with the negative x value is the points
[tex](0,-5)[/tex]