An ellipse has vertices along the major axis at (0, 1) and (0, −9). The foci of the ellipse are located at (0, −1) and (0, −7). The equation of the ellipse is in the form below.
Accepted Solution
A:
so, with those points provided, notice the vertices are lying along the y-axis, check the picture below, thus is a vertical ellipse.
now, the center is half-way between the vertices, therefore it'd be at 0, -4, like in the picture in red.
the distance from the center to either foci, is "c", and that's c = 3.
the "a" component of the major axis is 5 units, now let's find the "b" component,
[tex]\bf \textit{ellipse, vertical major axis}
\\\\
\cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1
\qquad
\begin{cases}
center\ ( h, k)\\
vertices\ ( h, k\pm a)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2- b ^2}
\end{cases}\\\\
-------------------------------[/tex]