Question

what is the major axis of the ellipse (x-9)^2/25 + (y+2)^2/100 = 1

Answer 1

every elipse has the equation:
\[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2}=1\]
\[\frac{ y^2 }{ a^2 }+\frac{ x^2 }{ b^2 }=1\]
The first equation represents an elipse whose major axis is on the x-axis and the second equation represents an elipse whose major axis is on the y-axis.
The same is applied when the elipse ha sbeen pivoted :
\[\frac{ (x- \alpha )^2 }{ a^2 }+\frac{ (y- \beta)^2 }{ b^2 }=1\]
\[\frac{ (y- \beta )^2 }{ a^2 }+\frac{ (x- \alpha)^2 }{ b^2 }=1\]
Where the first equation represents the equation of a pivoted elipse with the focal axis parallel to the x-axis.
The second one represents a pivoted elipse whose focal axis is parallel to the y-axis.