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 is the distance from the center to the vertex and b is the distance from the center to the co-vertex.
From the given information:
a = 5 (distance from origin to vertex)
b = 4 (distance from origin to co-vertex)
Plugging these values into the equation, we get:
(x^2/5^2) + (y^2/4^2) = 1
Simplifying:
(x^2/25) + (y^2/16) = 1
Therefore, the equation of the ellipse in standard form is:
x^2/25 + y^2/16 = 1