Method to find the equation of the axes of an ellipse

for general equation of ellipse

(x/a)^2 + (y/b)^2 = 1

where a>b

now the axis of this equation is y axis which numerator of a

similarily from givene expanded equation of ellipse complete the squares and get it in the general form

and in palce of x and y

we get something kind of ax+by + c

now the equation of axis will be that whose denominator is large

Hope this helps you, With an example,

1.Write an equation for the ellipse having one focus at (0, 3), a vertex at (0, 4), 
and its center at (0, 0).

2.Write an equation for the ellipse with vertices (4, 0) and (–2, 0) 
and foci (3, 0) and (–1, 0).
3.Write an equation for the ellipse centered at the origin, having a vertex at (0, –5) and containing the point (–2, 4)

4.Write an equation for the ellipse having foci at (–2, 0) and (2, 0) 
and eccentricity e = 3/4. 

Answer

An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant

the standard equation of an ellipse is (x/a)^2+(y/b)^2=1

the number "a" is the semi major axis

the number "b"is the semi minor axis

x,y are the any points on the ellipse