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)A. x^2/25 + y^2/16 = 1 B. x^2/16 + y^2/25 = 1 C. x^2/5 + y^2/4 = 1D. x^2/4 + y^2/5 = 1

The standard form equation of an ellipse with a horizontal major axis with center at (h,k), vertices at (a+k,k) and co-vertices at (h, b+k), is:
(x-h)^2/a^2+(y-k)^2/b^2=1
where a>b
given:
vertex at (-5,0)
co-vertex at (0,4)
vertex (a+h,k) so (a+h)=-5 and k=0
co-vertex (h, b+k); so h=0 and b+k=4
if h=0 then a+0=-5 which implies a=-4 and -a=5
if k=0, then b+0=4 and -b=-4
thus the equation will be:
(x-0)^2/5^2+(y-0)^2/4^2=1
this can be written as:
x^2/25+y^2/16=1