Question

Pre cal help
Eclipse IV

Answer 1

the standard form of ellipse is:
\[\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\]
where (h,k) is center of ellipse

The center is always the midpoint between the 2 vertices.
For example #1, we have (-5,4) and (8,4) as vertices
\[midpoint = (\frac{-5+8}{2}, \frac{4+4}{2}) = (1.5,4)\]
a = 8-1.5 = 6.5
"c" is length from center to focus point (-4,4)
c = 1.5 - (-4) = 5.5
\[b^2 = a^2 - c^2 = 6.5^2 - 5.5^2 = \frac{27}{2}\]