SOLUTION: An ellipse has a vertex at (0, �5), a co-vertex at (�3, 0), and a center at the origin. Which is the equation of the ellipse in standard form?

Question 890498: An ellipse has a vertex at (0, �5), a co-vertex at (�3, 0), and a center at the origin. Which is the equation of the ellipse in standard form?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
vertex at (0,-5) and at (-3,0).
center at the origin.

if the center is at the origin, then the horizontal vertex are at (0,-5) and (0,5).

the vertical vertex are at (-3,0) and (3,0)

a is the distance from the horizontal vertex to the center.
a = 5
b is the distance from the vertical vertex to the center.
b = 3.

c^2 is equal to the absolute value of (a^2 - b^2) = |25-9| = 16.
that makes c = 4.
c is the distance from the focus to the center of the ellipse.

the focus points of your ellipse are at (-4,0) and (4,0).

the focus points are always on the major axis.
the major axis of the ellipse is the longer axis which is the horizontal axis.

the standard, or vertex form of your ellipse would be:

x^2 / 25 + y^2 / 9 = 1

a picture of your ellipse is shown below:

$$$

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