What is the equation of the ellipse centered at the origin with a vertex at (0,3)

Question

and co-vertex at (-2,0)?

Answer 1

The center of the ellipse =origin = (0 , 0)

The vertex of the ellipse =(0 , a) =  (0 , 3)

                                                       a = 3

The co-vertex of the ellipse = (-b, 0) = (-2 , 0)

                                                         b = 2

The center origin then the equation of the ellipse = x² / b² + y² / a² = 1

Substitute a = 3 , b =2 in the ellipse equation

                                                                                          x² / 2² + y² / 3² = 1

                                                                                            x² / 4 + y² / 9 = 1.