Question

Ellipses- Given the Vertices and the Foci how can one find the equation of the ellipse? Please give an example.

Answer 1

Write an equation for the ellipse having one focus at (0, 3), a vertex at (0, 4),
and its center at (0, 0).
Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide. \[a^2\] will go with the y part of the equation. Also, since the focus is 3 units above the center, then c = 3; since the vertex is 4 units above, then \[a=4 \]
The equation \[b^2 = a^2 – c^2 \] gives me\[ 16 – 9 = 7 = b^2 \]. (Since I wasn't asked for the length of the minor axis or the location of the co-vertices, I don't need the value of b itself.)
\[\frac { y^{ 2 } }{ 16 } +\frac { { x }^{ 2 } }{ 7 } =1 \]

Answer 2

@TrigSucksDaww Is there any need to explain further

Answer 3

Yes, Vertices (+-9,0) Foci (+-6*Sqrt(2),0)