SOLUTION: Pls help me solve : given the with equation 25x^2+16y^2=400 .find the i) length of the major axis,ii)the length of the minor axis,iii) eccentricity, iv)coordinate of the foci,v)

You are given

 = 400.


Divide by 400 both sides.  You will get

 +  = 1,    or, which is the same

 +  = 1,    or,  which is the same


 +  = 1.     (1)


Equation (1) is the standard equation of an ellipse.


The ellipse is centered at the coordinate origin (0,0).

It has the major axis parallel to y-axis,

   so the ellipse is taller than wide.


Its major semi-axis has the length of 5 units,

while the minor semi-axis is of 4 units long.


The vertices are (0,5), (0,-5),   (-3,0), (3,0).


The linear eccentricity of the ellipse is  =  =  = 3.


The foci are  (0,3)  and  (0,-3).