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 general equation of an ellipse with center at the origin is:
(x^2/a^2) + (y^2/b^2) = 1
where a and b are the lengths of the semi-major and semi-minor axes, respectively.
To find these values, we need to use the given characteristics:
The distance from the center to a vertex is a, so a = 5.
The distance from the center to a co-vertex is b, so b = 4.
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