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 standard form of the equation of an ellipse centered at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where (a, 0) is the vertex and (0, b) is the co-vertex.
Given that the vertex is at (-5, 0) and the co-vertex is at (0, 4), we have:
a = 5 and b = 4
Plugging these values into the equation, we get:
(x^2/25) + (y^2/16) = 1
So, the equation of the ellipse in standard form is:
(x^2/25) + (y^2/16) = 1