The general equation of the ellipse is
[tex] \frac{ (x-h)^{2} }{ a^{2} } + \frac{ (y-k)^{2} }{ b^{2} } =1[/tex]
where (h,k) the coordinates of the center
a and b represents half the length of the axes
given: center of the ellipse = (0,0)
vertex (-5 , 0) and co-vertex (0 , -3)
∴ (h,k) = (0,0)
∴ a = 5 and b = 3
So, The equation in standard form of the ellipse is
[tex] \frac{ x^{2} }{ 25 } + \frac{ y^{2} }{ 9 } =1[/tex]
