The standard form of the equation for an ellipse centered at the origin is:
+=1where
a and
b are the lengths of the semi-major and semi-minor axes, respectively. The vertices of the ellipse are located at
(±a,0) and
(0,±b).
In this problem, we are given the vertices
(5,0) and
(0,−4), which correspond to the points
(a,0) and
(0,−b), respectively. So we have:
a=5 and
b=4Substituting these values into the standard form of the equation for an ellipse, we get:
+=1Simplifying and rearranging, we get:
+=1So the equation of the ellipse is
boxed+=1.