An ellipse has a vertex at (3, 0), a co-vertex at (0, −1), and a center at the origin. Which is the equation of the ellipse in standard form?
The standard form equation of an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
In this case, the vertex is at (3, 0) and the co-vertex is at (0, -1).
Since the center is at the origin, the distance from the center to the vertex is the length of the semi-major axis, a.
Therefore, a = 3.
The distance from the center to the co-vertex is the length of the semi-minor axis, b.
Therefore, b = 1.
Plugging these values into the standard form equation, we have:
(x^2/3^2) + (y^2/1^2) = 1
Simplifying, we get:
(x^2/9) + y^2 = 1
So, the equation of the ellipse in standard form is:
(x^2/9) + y^2 = 1