Write an equation of an ellipse in standard form with the center at the origin and with the given characteristics.
vertex at (–5, 0) and co-vertex at (0, 4)
The equation of an ellipse in standard form with the center at the origin is:
x^2/a^2 + y^2/b^2 = 1
where (a,b) are the lengths of the semi-major and semi-minor axes, respectively.
Given that the vertex is at (-5, 0) and the co-vertex is at (0, 4), we can determine that a = 5 and b = 4.
Therefore, the equation of the ellipse in standard form is:
x^2/5^2 + y^2/4^2 = 1
Simplifying:
x^2/25 + y^2/16 = 1
The equation of the ellipse in standard form with the center at the origin is:
x^2/25 + y^2/16 = 1