Question

state lengthof major and minor foci and center
(x^2)/4+(y^2)/25=1
i also need to learn how to graph it,thanks!

Answer 1

The standard equation of the ellipse with centre at (0,0) is
x^2/a^2 + y^2/b^2 = 1
yours fits that pattern, with a = 2 and b = 5
if a > b , the the major axis lies along the x-axis, otherwise it lies along the y-axis.

yours has its major axis along the y-axis
the vertices are (2,0), (-2,0), (0,5), and (0,-5)
and the centre is (0,0)

foci : (0,c) and (0,-c) such that
c^2 + 2^2 = 5^2
c^2 = 21
c = ± √21

I usually sketch an ellipse by drawing a rectangle with the vertices being the midpoints of the sides.
It is then generally easy to sketch the ellipse to fit inside that rectangle.
draw the rectangle with faint or dotted lines.